Using real fields instead of complex ones, it is suggested here that the fermions are pairs of coupled strings with an internal tension. The interaction between the two coupled strings is due to an exchange mechanism ...Using real fields instead of complex ones, it is suggested here that the fermions are pairs of coupled strings with an internal tension. The interaction between the two coupled strings is due to an exchange mechanism which is proportional to Planck’s constant. This may be the result of two massless bosons (hypergluons) coupled by a preon (prequark) exchange. It also gives a physical explanation to the origin of the Planck constant, and origin of spin.展开更多
Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s co...Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s constant. Quantum mechanics is described with real fields and real operators. Schrodinger and Dirac equations then are solved. The solution to Dirac equation gives four, real, 2-vectors solutions ψ1=(U1D1)ψ2=(U2D2)ψ3=(U3D3)ψ4=(U4D4)where (ψ1,ψ4) are coupled via linear combinations to yield spin-up and spin-down fermions. Likewise, (ψ2,ψ3) are coupled via linear combinations to represent spin-up and spin-down anti-fermions. For an incoming entangled pair of fermions, the combined solution is Ψin=c1ψ1+c4ψ4where c1and c4are some hidden variables. By applying a magnetic field in +Z and +x the theoretical results of a triple Stern-Gerlach experiment are predicted correctly. Then, by repeating Bell’s and Mermin Gedanken experiment with three magnetic filters σθ, at three different inclination angles θ, the violation of Bell’s inequality is proven. It is shown that all fermions are in a mixed state of spins and the ratio between spin-up to spin-down depends on the hidden variables.展开更多
Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix...Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected.展开更多
Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, neverthel...Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, nevertheless, our physical understanding of this process is nonintuitive at best. In this paper we analyze the creation of fermions from primordial gauge field quantum gravity loops in the context of Calabi-Yau manifold theory. I extend a prior mass-gap treatment based on Yang-Mills gauge theory of higher order self-interaction to include the half-integral spin of fermions.展开更多
We theoretically investigate the quantum interference theory of magnetotransport of the three-component or spin-1 chiral fermions, which possess two linear Dirac bands and a flat band. For isotropic scalar impurities,...We theoretically investigate the quantum interference theory of magnetotransport of the three-component or spin-1 chiral fermions, which possess two linear Dirac bands and a flat band. For isotropic scalar impurities, the correction of conductivity from the coherent backscatter and non-coherent backscatter contributions cancel out in the intravalley scattering, leading to a weak localization correction to the Drude conductivity from the intervalley scattering. For the anisotropic impurities, the above cancelation is removed, we find the approximative quantum interference conductivity in the weak anisotropy case. The contributions from the chiral anomaly and classical Lorentz force are also discussed. Our work reveals some intriguing and detectable transport signatures of the novel spin-1 chiral fermions.展开更多
We provide here an analytical formalism to describe the indirect interaction between adsorbed atom or molecule pairs mediated by two-dimensional(2D)Dirac fermions.We show that in contrast to the case of traditional 2D...We provide here an analytical formalism to describe the indirect interaction between adsorbed atom or molecule pairs mediated by two-dimensional(2D)Dirac fermions.We show that in contrast to the case of traditional 2D electron gas,in the 2D Dirac system,the long-range interaction behaves as 1/r^(3) decaying Friedel oscillation.This analytical formalism is fully consistent with a tight-binding numerical calculation of honeycomb lattices.Our formalism is suitable for the realistic 2D Dirac materials,such as graphene and surface states of three-dimensional topological insulators.展开更多
Two-dimensional honeycomb lattices show great potential in the realization of Dirac nodal line fermions(DNLFs).Here,we successfully synthesized a gold telluride(AuTe)monolayer by direct tellurizing an Au(111)substrate...Two-dimensional honeycomb lattices show great potential in the realization of Dirac nodal line fermions(DNLFs).Here,we successfully synthesized a gold telluride(AuTe)monolayer by direct tellurizing an Au(111)substrate.Low energy electron diffraction measurements reveal that it is(2×2)AuTe layer stacked onto(3×3)Au(111)substrate.Moreover,scanning tunneling microscopy images show that the AuTe layer has a honeycomb structure.Scanning transmission electron microscopy reveals that it is a single-atom layer.In addition,first-principles calculations demonstrate that the honeycomb AuTe monolayer exhibits Dirac nodal line features protected by mirror symmetry,which is validated by angle-resolved photoemission spectra.Our results establish that monolayer AuTe can be a good candidate to investigate 2D DNLFs and provides opportunities to realize high-speed low-dissipation devices.展开更多
This paper analyses the dispersion relation of the excitation mode in non-relativistic interacting fermion matter. The polarization tensor is calculated with the random phase approximation in terms of finite temperatu...This paper analyses the dispersion relation of the excitation mode in non-relativistic interacting fermion matter. The polarization tensor is calculated with the random phase approximation in terms of finite temperature field theory. With the polarization tensor, the influences of temperature, particle number density and interaction strength on the dispersion relation are discussed in detail. It finds that the collective effects are qualitatively more important in the unitary fermions than those in the finite contact interaction matter.展开更多
Heavy fermion materials are prototypical strongly correlated electron systems, where the strong electron–electron interactions lead to a wide range of novel phenomena and emergent phases of matter. Due to the low ene...Heavy fermion materials are prototypical strongly correlated electron systems, where the strong electron–electron interactions lead to a wide range of novel phenomena and emergent phases of matter. Due to the low energy scales, the relative strengths of the Ruderman–Kittel–Kasuya–Yosida(RKKY) and Kondo interactions can often be readily tuned by non-thermal control parameters such as pressure, doping, or applied magnetic fields, which can give rise to quantum criticality and unconventional superconductivity. Here we provide a brief overview of research into heavy fermion materials in high magnetic fields, focussing on three main areas. Firstly we review the use of magnetic fields as a tuning parameter,and in particular the ability to realize different varieties of quantum critical behaviors. We then discuss the properties of heavy fermion superconductors in magnetic fields, where experiments in applied fields can reveal the nature of the order parameter, and induce new novel phenomena. Finally we report recent studies of topological Kondo systems, including topological Kondo insulators and Kondo–Weyl semimetals. Here experiments in magnetic fields can be used to probe the topologically non-trivial Fermi surface, as well as related field-induced phenomena such as the chiral anomaly and topological Hall effect.展开更多
An effective relativistic continuum massive Proca Lagrangian action is used to account for the Lorentzvector condensation effects on the equation of state of the strongly interacting fermions system.The interior quant...An effective relativistic continuum massive Proca Lagrangian action is used to account for the Lorentzvector condensation effects on the equation of state of the strongly interacting fermions system.The interior quantumfluctuation effects are incorporated as an external field approximation indirectly through a fictive generalized ThomsonProblem counterterm background.The general analytical formulas for the d-dimensional thermodynamics are given nearthe unitary limit region,In the non-relativistic limit for d=3,the universal dimensionless coefficientε=4/9 andenergy gap △/ε_f=5/18 are reasonably consistent with the existing theoretical and experimental results.In the unitarylimit for d=2 and T=0,the universal coefficient can even approach the extreme occasion ξ=0 corresponding to theinfinite effective fermion mass m~*=∞,which can be mapped to the strongly coupled two-dimensional electrons and isquite similar to the three-dimensional Bose-Einstein condensation of ideal boson gas.Instead,for d=1,the universalcoefficient ξ is negative,implying the non-existence of phase transition from superfluidity to normal state.The solutionsmanifest the quantum Ising universal class characteristic of the strongly coupled unitary fermions gas.展开更多
We investigate theoretically Rabi-like splitting and Fano resonance in absorption spectra of quantum dots(QDs)based on a hybrid QD-semiconducting nanowire/superconductor(SNW/SC)device mediated by Majorana fermions(MFs...We investigate theoretically Rabi-like splitting and Fano resonance in absorption spectra of quantum dots(QDs)based on a hybrid QD-semiconducting nanowire/superconductor(SNW/SC)device mediated by Majorana fermions(MFs).Under the condition of pump on-resonance and off-resonance,the absorption spectrum experiences the conversion from Fano resonance to Rabi-like splitting in different parametric regimes.In addition,the Fano resonances are accompanied by the rapid normal phase dispersion,which will indicate the coherent optical propagation.The results indicate that the group velocity index is tunable with controlling the interaction between the QD and MFs,which can reach the conversion between the fast-and slow-light.Fano resonance will be another method to detect MFs and our research may indicate prospective applications in quantum information processing based on the hybrid QD-SNW/SC devices.展开更多
We describe a scheme for universal quantum computation with Majorana fermions. We investigate two possible dissipative couplings of Majorana fermions to external systems, including metallic leads and local phonons. Wh...We describe a scheme for universal quantum computation with Majorana fermions. We investigate two possible dissipative couplings of Majorana fermions to external systems, including metallic leads and local phonons. While the dissipation when coupling to metallic leads to uninteresting states for the Majorana fermions, we show that coupling the Majorana fermions to local phonons allows to generate arbitrary dissipations and therefore universal quantum operations on a single QuBit that can be enhanced by additional two-QuBit operations.展开更多
We try to explicitly derive the Lorentz-gauge covariant Dirac equation, in terms of pseudo-orthonormal bases, on Rindler spacetime and to work out, with all the necessary coefficients, the respective closed-form solut...We try to explicitly derive the Lorentz-gauge covariant Dirac equation, in terms of pseudo-orthonormal bases, on Rindler spacetime and to work out, with all the necessary coefficients, the respective closed-form solutions, in both Dirac and Weyl representations.展开更多
Quantum computers are in hot-spot with the potential to handle more complex problems than classical computers can.Realizing the quantum computation requires the universal quantum gate set {T,H,CNOT} so as to perform a...Quantum computers are in hot-spot with the potential to handle more complex problems than classical computers can.Realizing the quantum computation requires the universal quantum gate set {T,H,CNOT} so as to perform any unitary transformation with arbitrary accuracy.Here we first briefly review the Majorana fermions and then propose the realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions.Elementary cells consist of a quantum anomalous Hall insulator surrounded by a topological superconductor with electric gates and quantum-dot structures,which enable the braiding operation and the partial exchange operation.After defining a qubit by four chiral Majorana fermions,the singlequbit T and H quantum gates are realized via one partial exchange operation and three braiding operations,respectively.The entangled CNOT quantum gate is performed by braiding six chiral Majorana fermions.Besides,we design a powerful device with which arbitrary two-qubit quantum gates can be realized and take the quantum Fourier transform as an example to show that several quantum operations can be performed with this space-limited device.Thus,our proposal could inspire further utilization of mobile chiral Majorana edge states for faster quantum computation.展开更多
We have theoretically analyzed the quasibound states in a Mraphene quantum dot (GO, D) with a magnetic flux -φ in the centre. It is shown that the two-fold time reversal degeneracy is broken and the quasibound stat...We have theoretically analyzed the quasibound states in a Mraphene quantum dot (GO, D) with a magnetic flux -φ in the centre. It is shown that the two-fold time reversal degeneracy is broken and the quasibound states of GQD with positive^negative angular momentum shifted upwards/downwards with increasing the magnetic flux. The variation of the quasibound energy depends linearly on the magnetic flux, which is quite different from the parabolic relationship for SchrSdinger electrons. The GQD's quasibound states spectrum shows an obvious Aharonov-Bohm (AB) oscillations with the magnetic flux. It is also shown that the quasibound state with energy equal to the barrier height becomes a bound state completely confined in GQD.展开更多
We propose a two-component form to describe massive relativistic fermions in gauge theories. Relations between the Green's functions in this form and those in the conventional four-component form are derived. It is s...We propose a two-component form to describe massive relativistic fermions in gauge theories. Relations between the Green's functions in this form and those in the conventional four-component form are derived. It is shown that the S-matrix elements in both forms are exactly the same. The description of the fermion in the new form simplifies significantly the γ-matrix algebra in the four-component form. In particular, in perturbative calculations the propagator of the fermion is a scalar function. As examples, we use this form to reproduce the relativistic spectrum of hydrodron atom, the S-matrix of e+e-→μ+μ- and QED one-loop vacuum polarization of photon.展开更多
A matrix eigenvalue method is applied to analyse the thermodynamic stability of two-component interacting fermions. The non-relativistic and ultra-relativistic d = 1, 2, 3 dimensions have been discussed in detail, res...A matrix eigenvalue method is applied to analyse the thermodynamic stability of two-component interacting fermions. The non-relativistic and ultra-relativistic d = 1, 2, 3 dimensions have been discussed in detail, respectively. The corresponding stability region has been given according to the two-body interaction strength and the particle number density ratio.展开更多
The Dirac–Weyl equation characterized quasi-particles in the T3 lattice are studied under external magnetic field using the generalized uncertainty principle(GUP). The energy spectrum of the quasi-particles is found ...The Dirac–Weyl equation characterized quasi-particles in the T3 lattice are studied under external magnetic field using the generalized uncertainty principle(GUP). The energy spectrum of the quasi-particles is found by the Nikiforov–Uvarov method. Based on the energy spectrum obtained, the thermodynamic properties are given, and the influence of the GUP on the statistical properties of systems is discussed. The results show that the energy and thermodynamic functions of massless Dirac–Weyl fermions in the T3 lattice depend on the variation of the GUP parameter.展开更多
文摘Using real fields instead of complex ones, it is suggested here that the fermions are pairs of coupled strings with an internal tension. The interaction between the two coupled strings is due to an exchange mechanism which is proportional to Planck’s constant. This may be the result of two massless bosons (hypergluons) coupled by a preon (prequark) exchange. It also gives a physical explanation to the origin of the Planck constant, and origin of spin.
文摘Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s constant. Quantum mechanics is described with real fields and real operators. Schrodinger and Dirac equations then are solved. The solution to Dirac equation gives four, real, 2-vectors solutions ψ1=(U1D1)ψ2=(U2D2)ψ3=(U3D3)ψ4=(U4D4)where (ψ1,ψ4) are coupled via linear combinations to yield spin-up and spin-down fermions. Likewise, (ψ2,ψ3) are coupled via linear combinations to represent spin-up and spin-down anti-fermions. For an incoming entangled pair of fermions, the combined solution is Ψin=c1ψ1+c4ψ4where c1and c4are some hidden variables. By applying a magnetic field in +Z and +x the theoretical results of a triple Stern-Gerlach experiment are predicted correctly. Then, by repeating Bell’s and Mermin Gedanken experiment with three magnetic filters σθ, at three different inclination angles θ, the violation of Bell’s inequality is proven. It is shown that all fermions are in a mixed state of spins and the ratio between spin-up to spin-down depends on the hidden variables.
文摘Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected.
文摘Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, nevertheless, our physical understanding of this process is nonintuitive at best. In this paper we analyze the creation of fermions from primordial gauge field quantum gravity loops in the context of Calabi-Yau manifold theory. I extend a prior mass-gap treatment based on Yang-Mills gauge theory of higher order self-interaction to include the half-integral spin of fermions.
基金partially supported by the High Magnetic Field Laboratory of Anhui Province,China。
文摘We theoretically investigate the quantum interference theory of magnetotransport of the three-component or spin-1 chiral fermions, which possess two linear Dirac bands and a flat band. For isotropic scalar impurities, the correction of conductivity from the coherent backscatter and non-coherent backscatter contributions cancel out in the intravalley scattering, leading to a weak localization correction to the Drude conductivity from the intervalley scattering. For the anisotropic impurities, the above cancelation is removed, we find the approximative quantum interference conductivity in the weak anisotropy case. The contributions from the chiral anomaly and classical Lorentz force are also discussed. Our work reveals some intriguing and detectable transport signatures of the novel spin-1 chiral fermions.
基金the National Natural Science Foundation of China(Grant Nos.11804028 and 12175023)the Fund from the State Key Laboratory of Petroleum Resources and Prospecting,China University of Petroleum(Grant No.PRP/DX-2210)。
文摘We provide here an analytical formalism to describe the indirect interaction between adsorbed atom or molecule pairs mediated by two-dimensional(2D)Dirac fermions.We show that in contrast to the case of traditional 2D electron gas,in the 2D Dirac system,the long-range interaction behaves as 1/r^(3) decaying Friedel oscillation.This analytical formalism is fully consistent with a tight-binding numerical calculation of honeycomb lattices.Our formalism is suitable for the realistic 2D Dirac materials,such as graphene and surface states of three-dimensional topological insulators.
基金Project supported by the National Key R&D Program of China (Grant No.2018YFA0305800)the National Natural Science Foundation of China (Grant Nos.61925111,61888102,and 52102193)+2 种基金the Strategic Priority Research Program of Chinese Academy of Sciences (Grant Nos.XDB28000000 and XDB30000000)CAS Project for Young Scientists in Basic Research (Grant No.YSBR-003)the Fundamental Research Funds for the Central Universities。
文摘Two-dimensional honeycomb lattices show great potential in the realization of Dirac nodal line fermions(DNLFs).Here,we successfully synthesized a gold telluride(AuTe)monolayer by direct tellurizing an Au(111)substrate.Low energy electron diffraction measurements reveal that it is(2×2)AuTe layer stacked onto(3×3)Au(111)substrate.Moreover,scanning tunneling microscopy images show that the AuTe layer has a honeycomb structure.Scanning transmission electron microscopy reveals that it is a single-atom layer.In addition,first-principles calculations demonstrate that the honeycomb AuTe monolayer exhibits Dirac nodal line features protected by mirror symmetry,which is validated by angle-resolved photoemission spectra.Our results establish that monolayer AuTe can be a good candidate to investigate 2D DNLFs and provides opportunities to realize high-speed low-dissipation devices.
基金Project supported by the Scientific Starting Research Fund of Central China Normal UniversityNational Natural Science Foundation of China (Grant Nos 10675052 and 10875050)MOE of China (Grant No IRT0624)
文摘This paper analyses the dispersion relation of the excitation mode in non-relativistic interacting fermion matter. The polarization tensor is calculated with the random phase approximation in terms of finite temperature field theory. With the polarization tensor, the influences of temperature, particle number density and interaction strength on the dispersion relation are discussed in detail. It finds that the collective effects are qualitatively more important in the unitary fermions than those in the finite contact interaction matter.
基金Project supported by the National Natural Science Foundation of China(Grant No.U1632275)the National Key R&D Program of China(Grant Nos.2017YFA0303100 and 2016YFA0300202)the Science Challenge Project of China(Grant No.TZ2016004)
文摘Heavy fermion materials are prototypical strongly correlated electron systems, where the strong electron–electron interactions lead to a wide range of novel phenomena and emergent phases of matter. Due to the low energy scales, the relative strengths of the Ruderman–Kittel–Kasuya–Yosida(RKKY) and Kondo interactions can often be readily tuned by non-thermal control parameters such as pressure, doping, or applied magnetic fields, which can give rise to quantum criticality and unconventional superconductivity. Here we provide a brief overview of research into heavy fermion materials in high magnetic fields, focussing on three main areas. Firstly we review the use of magnetic fields as a tuning parameter,and in particular the ability to realize different varieties of quantum critical behaviors. We then discuss the properties of heavy fermion superconductors in magnetic fields, where experiments in applied fields can reveal the nature of the order parameter, and induce new novel phenomena. Finally we report recent studies of topological Kondo systems, including topological Kondo insulators and Kondo–Weyl semimetals. Here experiments in magnetic fields can be used to probe the topologically non-trivial Fermi surface, as well as related field-induced phenomena such as the chiral anomaly and topological Hall effect.
基金the Scientific Starting Research Fund of Central China Normal UniversityNational Natural Science Foundation of China under Grant No.10675052
文摘An effective relativistic continuum massive Proca Lagrangian action is used to account for the Lorentzvector condensation effects on the equation of state of the strongly interacting fermions system.The interior quantumfluctuation effects are incorporated as an external field approximation indirectly through a fictive generalized ThomsonProblem counterterm background.The general analytical formulas for the d-dimensional thermodynamics are given nearthe unitary limit region,In the non-relativistic limit for d=3,the universal dimensionless coefficientε=4/9 andenergy gap △/ε_f=5/18 are reasonably consistent with the existing theoretical and experimental results.In the unitarylimit for d=2 and T=0,the universal coefficient can even approach the extreme occasion ξ=0 corresponding to theinfinite effective fermion mass m~*=∞,which can be mapped to the strongly coupled two-dimensional electrons and isquite similar to the three-dimensional Bose-Einstein condensation of ideal boson gas.Instead,for d=1,the universalcoefficient ξ is negative,implying the non-existence of phase transition from superfluidity to normal state.The solutionsmanifest the quantum Ising universal class characteristic of the strongly coupled unitary fermions gas.
基金supported by the National Natural Science Foundation of China(Grant Nos.11804004 and 11647001)the China Postdoctoral Science Foundation(Grant No.2020M681973)Anhui Provincial Natural Science Foundation,China(Grant No.1708085QA11)。
文摘We investigate theoretically Rabi-like splitting and Fano resonance in absorption spectra of quantum dots(QDs)based on a hybrid QD-semiconducting nanowire/superconductor(SNW/SC)device mediated by Majorana fermions(MFs).Under the condition of pump on-resonance and off-resonance,the absorption spectrum experiences the conversion from Fano resonance to Rabi-like splitting in different parametric regimes.In addition,the Fano resonances are accompanied by the rapid normal phase dispersion,which will indicate the coherent optical propagation.The results indicate that the group velocity index is tunable with controlling the interaction between the QD and MFs,which can reach the conversion between the fast-and slow-light.Fano resonance will be another method to detect MFs and our research may indicate prospective applications in quantum information processing based on the hybrid QD-SNW/SC devices.
文摘We describe a scheme for universal quantum computation with Majorana fermions. We investigate two possible dissipative couplings of Majorana fermions to external systems, including metallic leads and local phonons. While the dissipation when coupling to metallic leads to uninteresting states for the Majorana fermions, we show that coupling the Majorana fermions to local phonons allows to generate arbitrary dissipations and therefore universal quantum operations on a single QuBit that can be enhanced by additional two-QuBit operations.
文摘We try to explicitly derive the Lorentz-gauge covariant Dirac equation, in terms of pseudo-orthonormal bases, on Rindler spacetime and to work out, with all the necessary coefficients, the respective closed-form solutions, in both Dirac and Weyl representations.
基金Project supported by the National Key R&D Program of China(Grant No.2017YFA0303301)the National Natural Science Foundation of China(Grant No.11921005)+1 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB28000000)Beijing Municipal Science&Technology Commission,China(Grant No.Z191100007219013)。
文摘Quantum computers are in hot-spot with the potential to handle more complex problems than classical computers can.Realizing the quantum computation requires the universal quantum gate set {T,H,CNOT} so as to perform any unitary transformation with arbitrary accuracy.Here we first briefly review the Majorana fermions and then propose the realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions.Elementary cells consist of a quantum anomalous Hall insulator surrounded by a topological superconductor with electric gates and quantum-dot structures,which enable the braiding operation and the partial exchange operation.After defining a qubit by four chiral Majorana fermions,the singlequbit T and H quantum gates are realized via one partial exchange operation and three braiding operations,respectively.The entangled CNOT quantum gate is performed by braiding six chiral Majorana fermions.Besides,we design a powerful device with which arbitrary two-qubit quantum gates can be realized and take the quantum Fourier transform as an example to show that several quantum operations can be performed with this space-limited device.Thus,our proposal could inspire further utilization of mobile chiral Majorana edge states for faster quantum computation.
基金Support by National Science Foundation of China under Grant Nos. 60776067 and 10974011
文摘We have theoretically analyzed the quasibound states in a Mraphene quantum dot (GO, D) with a magnetic flux -φ in the centre. It is shown that the two-fold time reversal degeneracy is broken and the quasibound states of GQD with positive^negative angular momentum shifted upwards/downwards with increasing the magnetic flux. The variation of the quasibound energy depends linearly on the magnetic flux, which is quite different from the parabolic relationship for SchrSdinger electrons. The GQD's quasibound states spectrum shows an obvious Aharonov-Bohm (AB) oscillations with the magnetic flux. It is also shown that the quasibound state with energy equal to the barrier height becomes a bound state completely confined in GQD.
基金Supported by National Natural Science Foundation of China under Grant No. 10475103
文摘We propose a two-component form to describe massive relativistic fermions in gauge theories. Relations between the Green's functions in this form and those in the conventional four-component form are derived. It is shown that the S-matrix elements in both forms are exactly the same. The description of the fermion in the new form simplifies significantly the γ-matrix algebra in the four-component form. In particular, in perturbative calculations the propagator of the fermion is a scalar function. As examples, we use this form to reproduce the relativistic spectrum of hydrodron atom, the S-matrix of e+e-→μ+μ- and QED one-loop vacuum polarization of photon.
基金Project supported by the Scientific Starting Research Fund of Central China Normal University of Chinathe National Natural Science Foundation of China (Grant Nos 10675052 and 10875050)Ministry of Education of China (Grant No IRT0624)
文摘A matrix eigenvalue method is applied to analyse the thermodynamic stability of two-component interacting fermions. The non-relativistic and ultra-relativistic d = 1, 2, 3 dimensions have been discussed in detail, respectively. The corresponding stability region has been given according to the two-body interaction strength and the particle number density ratio.
基金the National Natural Science Foundation of China(Grant No.11565009)。
文摘The Dirac–Weyl equation characterized quasi-particles in the T3 lattice are studied under external magnetic field using the generalized uncertainty principle(GUP). The energy spectrum of the quasi-particles is found by the Nikiforov–Uvarov method. Based on the energy spectrum obtained, the thermodynamic properties are given, and the influence of the GUP on the statistical properties of systems is discussed. The results show that the energy and thermodynamic functions of massless Dirac–Weyl fermions in the T3 lattice depend on the variation of the GUP parameter.