We theoretically investigate the Zitterbewegung （ZB） behavior of electrons in the Bernevig-Hughes-Zhang model with a short laser pulse. To obtain a steady picture, we fix the electron on the Landau levels with a mag...We theoretically investigate the Zitterbewegung （ZB） behavior of electrons in the Bernevig-Hughes-Zhang model with a short laser pulse. To obtain a steady picture, we fix the electron on the Landau levels with a magnetic field. The ZB motion and the electromagnetic radiations in the quantum spin Hall regime are given. We find that over a shorter time, the electromagnetic radiations show a quasi-classical cyclotron oscillation, while over a longer time, they exhibit a clear revival picture. The resulting revival time and excited electric field are large enough to make experimental detection accessible.展开更多
In terms of the volume-integrated Poynting vector, we present a quantum field-theory investigation of the zitterbewegung （ZB） of photons, and show that this ZB occurs only in the presence of virtual longitudinal and...In terms of the volume-integrated Poynting vector, we present a quantum field-theory investigation of the zitterbewegung （ZB） of photons, and show that this ZB occurs only in the presence of virtual longitudinal and scalar photons. To present a heuristic explanation for such a ZB, by assuming that the space time is sufficiently close to the flat Minkowski space, we show that the gravitational interaction can result in the ZB of photons.展开更多
The spin-magnetic moment of the electron is revisited. In the form of the relativistic quantum mechanics, we calculate the magnetic moment of Dirac electron with no orbital angular-momentum. It is inferred that obtain...The spin-magnetic moment of the electron is revisited. In the form of the relativistic quantum mechanics, we calculate the magnetic moment of Dirac electron with no orbital angular-momentum. It is inferred that obtained magnetic moment may be the spin-magnetic moment, because it is never due to orbital motion. A transition current flowing from a positive energy state to a negative energy state in Dirac Sea is found. Application to the band structure of semiconductor is suggested.展开更多
Quantum particles are assumed to have a path constituting a random fluctuation super imposed on a classical one resulting in a golden mean spiral propagating in spacetime. Consequently, the dimension of the path of th...Quantum particles are assumed to have a path constituting a random fluctuation super imposed on a classical one resulting in a golden mean spiral propagating in spacetime. Consequently, the dimension of the path of the quantum particle is given by one plus the random Cantor set Zitterbewegung, i.e. 1+Øwhere Øis the golden mean Hausdorff dimension of a random Cantor set. Proceeding in this way, we can derive the basic topological invariants of the corresponding spacetime which turned out to be that of E-infinity spacetime 4+Ø3 as well as a fractal Witten’s M-theory 11+Ø5. Setting Ø3 and Ø5 equal zero, we retrieve Einstein’s spacetime and Witten’s M-theory spacetime respectively where Ø3 is the latent Casimir topological pressure of spacetime and Ø5 is Hardy’s quantum entanglement of the same.展开更多
Assuming the Dirac wavefunction describes the state of a single particle. We propose that the relation derived by Schrödinger, which contains the Zitterbewegung term, is a position equation for an amplitude m...Assuming the Dirac wavefunction describes the state of a single particle. We propose that the relation derived by Schrödinger, which contains the Zitterbewegung term, is a position equation for an amplitude modulated wave. Namely, the elementary constituents are amplitude modulated waves. Indeed, we surmise that a second wave is associated with the particle, which corresponds to a signal. At the same time, we interpret that Broglie’s wave corresponds to a carrier. Furthermore, the quantum object is a recording medium and, like in a hologram, information encoded on its surface. We suggest a description and the cause of the Zitterbewegung heretofore never considered regarding the previous assertions. Hereunder, we shall also apply the quantum amplitude modulation interpretation to the single-photon wave function by Bialynicki-Birula. The predictions are testable, thence providing evidence for the proposed hypothesis.展开更多
Traditionally, all the discussions relativistic quantum mechanics. In this article, on zitterbewegung （zbw） of electron are based on from the viewpoint of quantum field theory and in terms of the creation and annihi...Traditionally, all the discussions relativistic quantum mechanics. In this article, on zitterbewegung （zbw） of electron are based on from the viewpoint of quantum field theory and in terms of the creation and annihilation operators as well as the polarization vectors of spin-1 field, a more detailed description and some new perspectives for zbw are obtained. Especially, it is shown that zbw arises from a to-and-fro vacuum polarization that occurring in the neighborhood of electron; the zbw vectors form a vector triplet with total spin projections 0 and ±1 in the direction of the momentum of electron, respectively; the macroscopic velocity of the vacuum medium vanishes in all inertial systems.展开更多
The motional trembling(‘zitterbewegung’)of a relativistic electron governed by Dirac equation was originally predicted by Schr¨odinger in the early days of quantum mechanics and simulated in a recent experiment...The motional trembling(‘zitterbewegung’)of a relativistic electron governed by Dirac equation was originally predicted by Schr¨odinger in the early days of quantum mechanics and simulated in a recent experiment with a single trapped ultracold ion.We investigate stable and instable confinements of a single trapped ion in a Paul trap under different conditions relevant to parity.Since our treatment involves neither restriction of Lamb-Dicke limit nor rotating-wave approximation,we may demonstrate different quantum dynamics of the single trapped ion in a wide range of the trapping parameters.We discuss the origin of the zitterbewegung which is relevant to the stability of the ion trapping.展开更多
We show that Bogoliubov's quasiparticle in superfluid 3He-B undergoes the Zitterbewegung, as a free relativistic Dirac's electron does. The expectation value of position, as well as spin, of the quasiparticle ...We show that Bogoliubov's quasiparticle in superfluid 3He-B undergoes the Zitterbewegung, as a free relativistic Dirac's electron does. The expectation value of position, as well as spin, of the quasiparticle is obtained and compared with that of the Dirac's electron. In particular, the Zitterbewegung of Bogoliubov's quasiparticle has a frequency approximately 105 lower than that of an electron, rendering a more promising experimental observation.展开更多
In this paper, we delve into the intrinsic nature of mass and gravity, as per the amplitude modulation interpretation of the quantum theory. We explore the idea that the elementary constituent is an electromagnetic co...In this paper, we delve into the intrinsic nature of mass and gravity, as per the amplitude modulation interpretation of the quantum theory. We explore the idea that the elementary constituent is an electromagnetic configuration that interacts with the quantum field, leading to the emergence of inertia and gravity as a reaction to the exchange with the quantum field. While these two phenomena have a common origin, they are distinct. Our proposal suggests manipulating the connection between the quantum field and the particle using high-frequency electromagnetic fields, thereby making a warp drive possible.展开更多
A new form of Dirac equation of a second order partial differential equation is found. With this wave equation the quivering motion (Zitterbewegung) is satisfactorily explained. A quaternionic analogue of Dirac equati...A new form of Dirac equation of a second order partial differential equation is found. With this wave equation the quivering motion (Zitterbewegung) is satisfactorily explained. A quaternionic analogue of Dirac equation is presented and compared with the ordinary Dirac equation. The two equations become the same if we replace the particle rest mass, m0, in the latter by im0. New space and time transformations in which these two equations represent a massless particle are found. The invariance of Klein-Gordon equation under these transformations yields the Dirac equation. The electron is found to be represented by a superposition of two waves with a group velocity equals to speed of light in vacuum.展开更多
We utilize the topological-geometrical structure imposed by the Heterotic superstring theory on spacetime in conjunction with the K3 Kähler manifold to explain the mysterious nature of dark matter and its cou...We utilize the topological-geometrical structure imposed by the Heterotic superstring theory on spacetime in conjunction with the K3 Kähler manifold to explain the mysterious nature of dark matter and its coupling to the pure dark energy density of the cosmos. The analogous situations in the case of a Kerr black hole as well as the redundant components of the Riemannian tensor are pointed out and the final result was found to be in complete agreement with all previous theoretical ones as well as all recent accurate measurements and cosmic observations. We conclude by commenting briefly on the Cantorian model of Zitterbewegung and the connection between Olbers’s paradox and dark energy.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11247204 and 61178032)the Fundamental Research Funds for the Central Universities,China(Grant No.JUSRP 11211)
文摘We theoretically investigate the Zitterbewegung （ZB） behavior of electrons in the Bernevig-Hughes-Zhang model with a short laser pulse. To obtain a steady picture, we fix the electron on the Landau levels with a magnetic field. The ZB motion and the electromagnetic radiations in the quantum spin Hall regime are given. We find that over a shorter time, the electromagnetic radiations show a quasi-classical cyclotron oscillation, while over a longer time, they exhibit a clear revival picture. The resulting revival time and excited electric field are large enough to make experimental detection accessible.
基金supported by the Fundamental Research Funds for the Central Universities (Grant No.ZYGX2010X013)
文摘In terms of the volume-integrated Poynting vector, we present a quantum field-theory investigation of the zitterbewegung （ZB） of photons, and show that this ZB occurs only in the presence of virtual longitudinal and scalar photons. To present a heuristic explanation for such a ZB, by assuming that the space time is sufficiently close to the flat Minkowski space, we show that the gravitational interaction can result in the ZB of photons.
文摘The spin-magnetic moment of the electron is revisited. In the form of the relativistic quantum mechanics, we calculate the magnetic moment of Dirac electron with no orbital angular-momentum. It is inferred that obtained magnetic moment may be the spin-magnetic moment, because it is never due to orbital motion. A transition current flowing from a positive energy state to a negative energy state in Dirac Sea is found. Application to the band structure of semiconductor is suggested.
文摘Quantum particles are assumed to have a path constituting a random fluctuation super imposed on a classical one resulting in a golden mean spiral propagating in spacetime. Consequently, the dimension of the path of the quantum particle is given by one plus the random Cantor set Zitterbewegung, i.e. 1+Øwhere Øis the golden mean Hausdorff dimension of a random Cantor set. Proceeding in this way, we can derive the basic topological invariants of the corresponding spacetime which turned out to be that of E-infinity spacetime 4+Ø3 as well as a fractal Witten’s M-theory 11+Ø5. Setting Ø3 and Ø5 equal zero, we retrieve Einstein’s spacetime and Witten’s M-theory spacetime respectively where Ø3 is the latent Casimir topological pressure of spacetime and Ø5 is Hardy’s quantum entanglement of the same.
文摘Assuming the Dirac wavefunction describes the state of a single particle. We propose that the relation derived by Schrödinger, which contains the Zitterbewegung term, is a position equation for an amplitude modulated wave. Namely, the elementary constituents are amplitude modulated waves. Indeed, we surmise that a second wave is associated with the particle, which corresponds to a signal. At the same time, we interpret that Broglie’s wave corresponds to a carrier. Furthermore, the quantum object is a recording medium and, like in a hologram, information encoded on its surface. We suggest a description and the cause of the Zitterbewegung heretofore never considered regarding the previous assertions. Hereunder, we shall also apply the quantum amplitude modulation interpretation to the single-photon wave function by Bialynicki-Birula. The predictions are testable, thence providing evidence for the proposed hypothesis.
基金China National Natural Science Foundation and the Excellent Young Teachers Program of MOE of China (No. 69971008)
文摘Traditionally, all the discussions relativistic quantum mechanics. In this article, on zitterbewegung （zbw） of electron are based on from the viewpoint of quantum field theory and in terms of the creation and annihilation operators as well as the polarization vectors of spin-1 field, a more detailed description and some new perspectives for zbw are obtained. Especially, it is shown that zbw arises from a to-and-fro vacuum polarization that occurring in the neighborhood of electron; the zbw vectors form a vector triplet with total spin projections 0 and ±1 in the direction of the momentum of electron, respectively; the macroscopic velocity of the vacuum medium vanishes in all inertial systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.11274352 and 11274351)
文摘The motional trembling(‘zitterbewegung’)of a relativistic electron governed by Dirac equation was originally predicted by Schr¨odinger in the early days of quantum mechanics and simulated in a recent experiment with a single trapped ultracold ion.We investigate stable and instable confinements of a single trapped ion in a Paul trap under different conditions relevant to parity.Since our treatment involves neither restriction of Lamb-Dicke limit nor rotating-wave approximation,we may demonstrate different quantum dynamics of the single trapped ion in a wide range of the trapping parameters.We discuss the origin of the zitterbewegung which is relevant to the stability of the ion trapping.
基金supported by NSF of China under Grant No.11105097supported by National Basic Research Program(973 Program) of China under Grant No.2012CB921900+1 种基金NSF of China under Grant Nos.11175089 and 11475089partly supported by National Research Foundation and Ministry of Education,Singapore
文摘We show that Bogoliubov's quasiparticle in superfluid 3He-B undergoes the Zitterbewegung, as a free relativistic Dirac's electron does. The expectation value of position, as well as spin, of the quasiparticle is obtained and compared with that of the Dirac's electron. In particular, the Zitterbewegung of Bogoliubov's quasiparticle has a frequency approximately 105 lower than that of an electron, rendering a more promising experimental observation.
文摘In this paper, we delve into the intrinsic nature of mass and gravity, as per the amplitude modulation interpretation of the quantum theory. We explore the idea that the elementary constituent is an electromagnetic configuration that interacts with the quantum field, leading to the emergence of inertia and gravity as a reaction to the exchange with the quantum field. While these two phenomena have a common origin, they are distinct. Our proposal suggests manipulating the connection between the quantum field and the particle using high-frequency electromagnetic fields, thereby making a warp drive possible.
文摘A new form of Dirac equation of a second order partial differential equation is found. With this wave equation the quivering motion (Zitterbewegung) is satisfactorily explained. A quaternionic analogue of Dirac equation is presented and compared with the ordinary Dirac equation. The two equations become the same if we replace the particle rest mass, m0, in the latter by im0. New space and time transformations in which these two equations represent a massless particle are found. The invariance of Klein-Gordon equation under these transformations yields the Dirac equation. The electron is found to be represented by a superposition of two waves with a group velocity equals to speed of light in vacuum.
文摘We utilize the topological-geometrical structure imposed by the Heterotic superstring theory on spacetime in conjunction with the K3 Kähler manifold to explain the mysterious nature of dark matter and its coupling to the pure dark energy density of the cosmos. The analogous situations in the case of a Kerr black hole as well as the redundant components of the Riemannian tensor are pointed out and the final result was found to be in complete agreement with all previous theoretical ones as well as all recent accurate measurements and cosmic observations. We conclude by commenting briefly on the Cantorian model of Zitterbewegung and the connection between Olbers’s paradox and dark energy.
