Dissipative dynamics of an entangled three-qubit system via non-Hermitian Hamiltonian: Its correspondence with Markovian and non-Markovian regimes

We investigate an entangled three-qubit system in which only one of the qubits experiences the decoherence effect by considering a non-Hermitian Hamiltonian,while the other two qubits are isolated,i.e.,do not interact with environment,directly.Then,the time evolution of the density matrix(for the pure as well as mixed initial density matrix)and the corresponding reduced density matrices are obtained,by which we are able to utilize the dissipative non-Hermitian Hamiltonian model with Markovian and non-Markovian regimes via adjusting the strange of the non-Hermitian term of the total Hamiltonian of the under-considered system.

Quantum exceptional points of non-Hermitian Hamiltonian and Liouvillian in dissipative quantum Rabi model

The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degeneracies in the open quantum system.Here,considering a dissipative quantum Rabi model,we study the spectral features of EPs in these two descriptions and explore their connections.We find that,although the EPs in these two descriptions are usually different,the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime.Further,we find that the quantum Fisher information(QFI),which measures the statistical distance between quantum states,can be used as a signature for the appearance of EPs.Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.

Application of non-Hermitian Hamiltonian model in open quantum optical systems

Non-Hermitian systems have observed numerous novel phenomena and might lead to various applications.Unlike standard quantum physics,the conservation of energy guaranteed by the closed system is broken in the non-Hermitian system,and the energy can be exchanged between the system and the environment.Here we present a scheme for simulating the dissipative phase transition with an open quantum optical system.The competition between the coherent interaction and dissipation leads to the second-order phase transition.Furthermore,the quantum correlation in terms of squeezing is studied around the critical point.Our work may provide a new route to explore the non-Hermitian quantum physics with feasible techniques in experiments.

Real Eigenvalue of a Non-Hermitian Hamiltonian System

With a view to getting further insight into the solutions of one-dimensional analogous Schr?dinger equation for a non-hermitian (complex) Hamiltonian system, we investigate the quasi-exact PT- symmetric solutions for an octic potential and its variant using extended complex phase space approach characterized by x=x1+ip2, p=p1+ix2, where (x1, p1) and (x2, p2) are real and considered as canonical pairs. Besides the complexity of the phase space, complexity of potential parameters is also considered. The analyticity property of the eigenfunction alone is found sufficient to throw light on the nature of eigenvalue and eigenfunction of a system. The imaginary part of energy eigenvalue of a non-hermitian Hamiltonian exist for complex potential parameters and reduces to zero for real parameters. However, in the present work, it is found that imaginary component of the energy eigenvalue vanishes even when potential parameters are complex, provided that PT-symmetric condition is satisfied. Thus PT- symmetric version of a non-hermitian Hamiltonian possesses the real eigenvalue.

Exceptional points and quantum dynamics in a non-Hermitian two-qubit system

We study the exceptional-point(EP) structure and the associated quantum dynamics in a system consisting of a non-Hermitian qubit and a Hermitian qubit. We find that the system possesses two sets of EPs, which divide the systemparameter space into PT-symmetry unbroken, partially broken and fully broken regimes, each with distinct quantumdynamics characteristics. Particularly, in the partially broken regime, while the PT-symmetry is generally broken in the whole four-dimensional Hilbert space, it is preserved in a two-dimensional subspace such that the quantum dynamics in the subspace are similar to those in the PT-symmetry unbroken regime. In addition, we reveal that the competition between the inter-qubit coupling and the intra-qubit driving gives rise to a complex pattern in the EP variation with system parameters.

On traceable iterated line graph and hamiltonian path index

Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.

Anomalous time-reversal symmetric non-Hermitian systems

The conditions for the emergence of the non-Hermitian skin effect, as a unique physical response of non-Hermitian systems, have now become one of the hot research topics. In this paper, we study the novel physical responses of nonHermitian systems with anomalous time-reversal symmetry, in both one dimension and two dimensions. Specifically, we focus on whether the systems will exhibit a non-Hermitian skin effect. We employ the theory of generalized Brillouin zone and also numerical methods to show that the anomalous time-reversal symmetry can prevent the skin effect in onedimensional non-Hermitian systems, but is unable to exert the same effectiveness in two-dimensional cases.

Dynamical localization in a non-Hermitian Floquet synthetic system

We investigate the non-Hermitian effects on quantum diffusion in a kicked rotor model where the complex kicking potential is quasi-periodically modulated in the time domain.The synthetic space with arbitrary dimension can be created by incorporating incommensurate frequencies in the quasi-periodical modulation.In the Hermitian case,strong kicking induces the chaotic diffusion in the four-dimension momentum space characterized by linear growth of mean energy.We find that the quantum coherence in deep non-Hermitian regime can effectively suppress the chaotic diffusion and hence result in the emergence of dynamical localization.Moreover,the extent of dynamical localization is dramatically enhanced by increasing the non-Hermitian parameter.Interestingly,the quasi-energies become complex when the non-Hermitian parameter exceeds a certain threshold value.The quantum state will finally evolve to a quasi-eigenstate for which the imaginary part of its quasi-energy is large most.The exponential localization length decreases with the increase of the non-Hermitian parameter,unveiling the underlying mechanism of the enhancement of the dynamical localization by nonHermiticity.

Universal Machine Learning Kohn–Sham Hamiltonian for Materials

While density functional theory(DFT)serves as a prevalent computational approach in electronic structure calculations,its computational demands and scalability limitations persist.Recently,leveraging neural networks to parameterize the Kohn-Sham DFT Hamiltonian has emerged as a promising avenue for accelerating electronic structure computations.Despite advancements,challenges such as the necessity for computing extensive DFT training data to explore each new system and the complexity of establishing accurate machine learning models for multi-elemental materials still exist.Addressing these hurdles,this study introduces a universal electronic Hamiltonian model trained on Hamiltonian matrices obtained from first-principles DFT calculations of nearly all crystal structures on the Materials Project.We demonstrate its generality in predicting electronic structures across the whole periodic table,including complex multi-elemental systems,solid-state electrolytes,Moir´e twisted bilayer heterostructure,and metal-organic frameworks.Moreover,we utilize the universal model to conduct high-throughput calculations of electronic structures for crystals in GNoME datasets,identifying 3940 crystals with direct band gaps and 5109 crystals with flat bands.By offering a reliable efficient framework for computing electronic properties,this universal Hamiltonian model lays the groundwork for advancements in diverse fields,such as easily providing a huge data set of electronic structures and also making the materials design across the whole periodic table possible.

Majorana tunneling in a one-dimensional wire with non-Hermitian double quantum dots

The combination of non-Hermitian physics and Majorana fermions can give rise to new effects in quantum transport systems. In this work, we investigate the interplay of PT-symmetric complex potentials, Majorana tunneling and interdot tunneling in a non-Hermitian double quantum dots system. It is found that in the weak-coupling regime the Majorana tunneling has pronounced effects on the transport properties of such a system, manifested as splitting of the single peak into three and a reduced 1/4 peak in the transmission function. In the presence of the PT-symmetric complex potentials and interdot tunneling, the 1/4 central peak is robust against them, while the two side peaks are tuned by them. The interdot tunneling only induces asymmetry, instead of moving the conductance peak, due to the robustness of the Majorana modes. There is an exceptional point induced by the union of Majorana tunneling and interdot tunneling. With increased PT-symmetric complex potentials, the two side peaks will move towards each other. When the exceptional point is passed through, these two side peaks will disappear. In the strong-coupling regime, the Majorana fermion induces a 1/4 conductance dip instead of the three-peak structure. PT-symmetric complex potentials induce two conductance dips pinned at the exceptional point. These effects should be accessible in experiments.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

An Eight Component Integrable Hamiltonian Hierarchy from a Reduced Seventh-Order Matrix Spectral Problem

We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.

Variational Principle for a Schrodinger Equation with Non-Hermitian Hamiltonian and Position-Dependent Mass

A classical field theory for a Schrodinger equation with a non-Hermitian Hamiltonian describing a particle with position-dependent mass has been recently advanced by Nobre and Rego-Monteiro(NR)[Phys.Rev.A 88(2013)032105].This field theory is based on a variational principle involving the wavefunction Ψ(x,t) and an auxiliary fieldΦ{x,t).It is here shown that the relation between the dynamics of the auxiliary field Φ(x,t) and that of the original wavefunction Ψ(x,t) is deeper than suggested by the NR approach.Indeed,we formulate a variational principle for the aforementioned Schrodinger equation which is based solely on the wavefunction Ψ(x,t).A continuity equation for an appropriately defined probability density,and the concomitant preservation of the norm,follows from this variational principle via Noether's theorem.Moreover,the norm-conservation law obtained by NR is reinterpreted as tie preservation of the inner product between pairs of solutions of the variable mass Schrodinger equation.

分数阶Hamiltonian系统的可解性

研究一类分数阶Hamiltonian系统解的存在性.考虑含有参数的势函数W(t,u)满足新的超线性和次线性组合条件W(t,u)=W_(1)(t,u)+μW_(2)(t,u),μ>0.当|u|→∞时,W_(1)(t,u)满足更一般的超线性增长条件,代替Ambrosetti-Rabinowitz条件;W_(2)(t,u)满足更一般的次线性增长条件.这部分需要建立新的紧嵌入定理,用于验证序列的紧性.利用临界点理论,得到上述系统2个解存在结果.

Fast population transfer with a superconducting qutrit via non-Hermitian shortcut to adiabaticity

Non-Hermitian dissipation dynamics,capable of turning the conventionally detrimental decoherence effects to useful resources for state engineering,is highly attractive to quantum information processing.In this work,an effective scheme is developed for implementing fast population transfer with a superconducting qutrit via the non-Hermitian shortcut to adiabaticity(STA).We first deal with aΛ-configuration interaction between the qutrit and microwave drivings,in which the dephasing-assisted qubit state inversion requiring an overlarge dephasing rate is constructed non-adiabatically.After introducing a feasible ancillary driving that directly acts upon the qubit states,the target state transfer can be well realized but with an accessible qubit dephasing rate.Moreover,a high fidelity could be numerically obtained in the considered system.The strategy could provide a new route towards the non-Hermitian shortcut operations on superconducting quantum circuits.

New application of non-Hermitian Hamiltonian operator in solving master equation for laser process

We find that laser process can be equivalently described by a symplectic evolution in the context of thermo field dynamics, and the corresponding coherent state evolution for the corresponding master equation is recognized. More interestingly, this embodies a new application of non-Hermitian Hamiltonian operator which can well expose the entanglement between the system and its environment.

HAMILTON-JACOBI EQUATIONS FOR A REGULAR CONTROLLED HAMILTONIAN SYSTEM AND ITS REDUCED SYSTEMS

In this paper,we give the geometric constraint conditions of a canonical symplectic form and regular reduced symplectic forms for the dynamical vector fields of a regular controlled Hamiltonian(RCH)system and its regular reduced systems,which are called the Type I and Type II Hamilton-Jacobi equations.First,we prove two types of Hamilton-Jacobi theorems for an RCH system on the cotangent bundle of a configuration manifold by using the canonical symplectic form and its dynamical vector field.Second,we generalize the above results for a regular reducible RCH system with symmetry and a momentum map,and derive precisely two types of Hamilton-Jacobi equations for the regular point reduced RCH system and the regular orbit reduced RCH system.Third,we prove that the RCH-equivalence for the RCH system,and the RpCH-equivalence and RoCH-equivalence for the regular reducible RCH systems with symmetries,leave the solutions of corresponding Hamilton-Jacobi equations invariant.Finally,as an application of the theoretical results,we show the Type I and Type II Hamilton-Jacobi equations for the Rp-reduced controlled rigid body-rotor system and the Rp-reduced controlled heavy top-rotor system on the generalizations of the rotation group SO(3)and the Euclidean group SE(3),respectively.This work reveals the deeply internal relationships of the geometrical structures of phase spaces,the dynamical vector fields and the controls of the RCH system.

Mobility edges generated by the non-Hermitian flatband lattice

We study the cross-stitch flatband lattice subject to the quasiperiodic complex potential exp(ix). We firstly identify the exact expression of quadratic mobility edges through analytical calculation, then verify the theoretical predictions by numerically calculating the inverse participation ratio. Further more, we study the relationship between the real–complex spectrum transition and the localization–delocalization transition, and demonstrate that mobility edges in this non-Hermitian model not only separate localized from extended states but also indicate the coexistence of complex and real spectrum.

Hall conductance of a non-Hermitian two-band system with k-dependent decay rates

Two-band model works well for Hall effect in topological insulators. It turns out to be non-Hermitian when the system is subjected to environments, and its topology characterized by Chern numbers has received extensive studies in the past decades. However, how a non-Hermitian system responses to an electric field and what is the connection of the response to the Chern number defined via the non-Hermitian Hamiltonian remains barely explored. In this paper, focusing on a k-dependent decay rate, we address this issue by studying the response of such a non-Hermitian Chern insulator to an external electric field. To this aim, we first derive an effective non-Hermitian Hamiltonian to describe the system and give a specific form of k-dependent decay rate. Then we calculate the response of the non-Hermitian system to a constant electric field.We observe that the environment leads the Hall conductance to be a weighted integration of curvature of the ground band and hence the conductance is no longer quantized in general. And the environment induces a delay in the response of the system to the electric field. A discussion on the validity of the non-Hermitian model compared with the master equation description is also presented.

Observation of size-dependent boundary effects in non-Hermitian electric circuits

The non-Hermitian systems with the non-Hermitian skin effect(NHSE)are very sensitive to the imposed boundary conditions and lattice sizes,which lead to size-dependent non-Hermitian skin effects.Here,we report the experimental observation of NHSE with different boundary conditions and different lattice sizes in the unidirectional hopping model based on a circuit platform.The circuit admittance spectra and corresponding eigenstates are very sensitive to the presence of the boundary.Meanwhile,our experimental results show how the lattice sizes and boundary terms together affect the strength of NHSE.Therefore,our electric circuit provides a good platform to observe size-dependent boundary effects in non-Hermitian systems.