Chiral symmetry restoration and deconfinement in the contact interaction model of quarks with parallel electric and magnetic fields

We study the impact of steady,homogeneous,and external parallel electric and magnetic field strengths(eE ‖ eB) on the chiral symmetry breaking-restoration and confinement-deconfinement phase transition.We also sketch the phase diagram of quantum chromodynamics(QCD) at a finite temperature T and in the presence of background fields.The unified formalism for this study is based on the Schwinger-Dyson equations,symmetry preserving vector-vector contact interaction model of quarks,and an optimal time regularization scheme.At T=0,in the purely magnetic case(i.e.,eE→0),we observe the well-known magnetic catalysis effect.However,in a pure electric field background(eB→0),the electric field tends to restore the chiral symmetry and deconfinement above the pseudo-critical electric field eE_c~(χ,C).In the presence of both eE and eB,we determine the magnetic catalysis effect in the particular region where eB dominates over eE,whereas we observe the chiral inhibition(or electric chiral rotation) effect when eE overshadows eB.At finite T,in the pure electric field case,the phenomenon of inverse electric catalysis appears to exist in the proposed model.Conversely,for a pure magnetic field background,we observe the magnetic catalysis effect in the mean-field approximation and inverse magnetic catalysis with eB-dependent coupling.The combined effects of eE and eB on the pseudo-critical T_c~(χ,C) yields an inverse electromagnetic catalysis,with and without an eB-dependent effective coupling of the model.The findings of this study agree well with the already predicted results obtained via lattice simulations and other reliable effective models of QCD.     

The Klein-Gordon and the Dirac Oscillators in a Noncommutative Space

We study the Dirac and the Klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.     

Improvement in refractive-index change in LiNbO3：Ce：Cu by applying an external electric field

By jointly solving two-centre material equations with a nonzero external electric field and coupled-wave equations, we have numerically studied the dependence of the non-volatile holographic recording in LiNbO3：Ce：Cu crystals on the external electric field. The dominative photovoltaic effect of the non-volatile holographic recording in doubly doped LiNbO3 crystals is directly verified. And an external electric field that is applied in the positive direction along the c-axis （or a large one in the negative direction of the c-axis） in the recording phase and another one that is applied in the negative direction of the c-axis in the fixing phase are both proved to benefit strong photorefractive performances. Experimental verifications are given with a small electric field applied externally.     

An Exactly Solvable Spin-1 Model under External Magnetic Field

A two-fold Cayley tree with fully q-coordinated sites is constructed and the spin-1 Blume-Capel model in the presence of an external magnetic field is solved exactly. The relevant properties such as magnetization m and square magnetic moment q are investigated as functions of temperature and external magnetic fieId both for ferromagnetic and antiferromagnetic couplings. In the study, we propose a possible mechanism of the plateau based on the exchange couplings.     

Stimulated Raman Scattering in a Weakly Polar Ⅲ-Ⅴ Semiconductor： Effect of dc Magnetic Field and Free Carrier Concentration

Using the hydrodynamic model of semiconductor plasmas, we perform an analytical investigation of stimulated Raman scattering （SITS） of an electromagnetic pump wave in a transversely magnetized weakly polar semicon- ductor arising from electron-density perturbations and molecular vibrations of the medium both produced at the longitudinal optical phonon frequency. Assuming that the origin of SItS lies in the third-order susceptibility of the medium, we investigate the growth rate of Stokes mode. The dependence of stimulated Raman gain on the external dc magnetic field strength and free carrier concentration is reported. The possibility of the occurrence of optical phase conjugation via SItS is also studied. The steady-state Raman gain is found to be greatly enhanced by the presence of the strong external dc magnetic field.     

Magnetic field effect in photodetachment from negative ion in electric field near metal surface

Based on the closed-orbit theory, the magnetic field effect in the photodetachment of negative ion in the electric field near a metal surface is studied for the first time. The results show that the magnetic field can produce a significant effect on the photodetachment of negative ion near a metal surface. Besides the closed orbits previously found by Du et al. for the H in the electric field near a metal surface (J. Phys. B 43 035002 (2010)), some additional closed orbits are produced due to the effect of magnetic field. For a given ion-surface distance and an electric field strength, the cross section depends sensitively on the magnetic field strength. As the magnetic field strength is very small, its influence can be neglected. With the increase of the magnetic field strength, the number of the closed orbits increases greatly and the oscillation in the cross section becomes much more complex. Therefore we can control the photodetachment cross section of the negative ion by changing the magnetic field strength. We hope that our results may guide future experimental studies for the photodetachment process of negative ion in the presence of external fields and surfaces.     

Spin-1/2 relativistic particle in a magnetic field in NC phase space

This work provides an accurate study of the spin-l/2 relativistic particle in a magnetic field in NC phase space. By detailed calculation we find that the Dirac equation of the relativistic particle in a magnetic field in noncommutative space has similar behaviour to what happens in the Landau problem in commutative space even if an exact map does not exist. By solving the Dirac equation in NC phase space, we not only obtain the energy level of the spin-1/2 relativistic particle in a magnetic field in NC phase space but also explicitly offer some additional terms related to the momentum-momentum non-commutativity.     

Non-Commutative Fock--Darwin System and Magnetic Field Limits

A Fock--Darwin system in noncommutative quantum mechanics is studied. By constructing Heisenberg algebra we obtain the levels on noncommutative space and noncommutative phase space, and give the corrections to the results in usual quantum mechanics. Moreover, to search the difference among the three spaces, the degeneracy is analysed by two ways, the valueof ω/ω_c and certain algebra realization (SU(2)and SU(1,1)), and some interesting properties in the magnetic field limit are exhibited, such as totally different degeneracy and magic number distribution for the given frequency or mass of a system in strong magnetic field.     

Controlling Thermodynamic Properties of Ferromagnetic Group-Ⅳ Graphene-Like Nanosheets by Dilute Charged Impurity

Using the Kane-Mele Hamiltonian, Dirac theory and self-consistent Born approximation, we investigate the effect of dilute charged impurity on the electronic heat capacity and magnetic susceptibility of two-dimensional ferromagnetic honeycomb structure of group-Ⅳ elements including silicene, germanene and stanene within the Green's function approach. We also find these quantities in the presence of applied external electric field. Our results show that the silicene(stanene) has the maximum(minimum) heat capacity and magnetic susceptibility at uniform electric fields. From the behavior of theses quantities, the band gap has been changed with impurity concentration, impurity scattering strength and electric field. The analysis on the impurity-dependent magnetic susceptibility curves shows a phase transition from ferromagnetic to paramagnetic and antiferromagnetic phases. Interestingly, electronic heat capacity increases(decreases) with impurity concentration in silicene(germanene and stanene) structure.     

Quantum Phase for an Electric Multipole Moment in Noncommutative Quantum Mechanics

We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric multipole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations, we obtain quantum phases of the electric multipole moment both on a noncommutative space and a noncommutative phase space. We demonstrate that these phase are geometric and dispersive.     

The Aharonov–Bohm effect in noncommutative quantum mechanics

The Aharonov–Bohm effect in noncommutative (NC) quantum mechanics is studied. First, by introducing a shift for the magnetic vector potential we give the Schrödinger equations in the presence of a magnetic field on NC space and NC phase space, respectively. Then, by solving the Schrödinger equations, we obtain the Aharonov–Bohm phase on NC space and NC phase space, respectively.     

Quantum Hall effect in noncommutative quantum mechanics

We study the quantum Hall (QH) effect for an electron moving in a plane whose coordinates and momenta are noncommuting under the influence of uniform external magnetic and electric fields. After solving the time independent Schrödinger equation both on a noncommutative space (NCS) and a noncommutative phase space (NCPS), we obtain the energy eigenvalues and eigenfunctions of the relevant Hamiltonian. We derive the electric current whose expectation value gives the QH effect both on a NCS and a NCPS.     

The Schrödinger and Pauli-Dirac Oscillators in Noncommutative Phase Space

We investigate the non-relativistic Schrödinger and Pauli-Dirac oscillators in noncommutative phase space using the five-dimensional Galilean covariant framework. The Schrödinger oscillator presented the correct energy spectrum whose non isotropy is caused by the noncommutativity with an expected similarity between this system and the particle in a magnetic field. A general Hamiltonian for the 3-dimensional Galilean covariant Pauli-Dirac oscillator was obtained and it presents the usual terms that appears in commutative space, like Zeeman effect and spin-orbit terms. We find that the Hamiltonian also possesses terms involving the noncommutative parameters that are related to a type of magnetic moment and an electric dipole moment.     

Electron resonance dynamics in a double quantum well

We consider the two-level electron dynamics in a double quantum well in a periodic, anharmonic external electric field. We propose a method for solving the Schrödinger equation, which is based on the generalization of conventional resonance approximation for a system with an arbitrary number of resonances. The method is used for the case of both weak and strong fields. We obtain expressions for the quasi-energy wave functions and the electron dipole moment. It is shown that the dependence of the dipole moment on the constant component of external field is quasi-periodic, and the dipole moment changes sign at different half-periods.     

Model of a relativistic oscillator in a generalized Schrödinger picture

In a generalized Schrödinger picture, we consider the motion of a relativistic particle in an external field (like in the case of a harmonic oscillator). In this picture the analogs of the Schrödinger operators of the particle are independent of both the time and the space coordinates. These operators induce operators which are related to Killing vectors of the Anti de Sitter (AdS) space. We also consider the nonrelativistic limit.     

Prequantum Classical Statistical Field Theory: Complex Representation, Hamilton-Schrödinger Equation, and Interpretation of Stationary States

We develop a prequantum classical statistical model in that the role of hidden variables is played by classical (vector) fields. We call this model Prequantum Classical Statistical Field Theory (PCSFT). The correspondence between classical and quantum quantities is asymptotic, so we call our approach asymptotic dequantization. We construct the complex representation of PCSFT. In particular, the conventional Schrödinger equation is obtained as the complex representation of the system of Hamilton equations on the infinite-dimensional phase space. In this note we pay the main attention to interpretation of so called pure quantum states (wave functions) in PCSFT, especially stationary states. We show, see Theorem 2, that pure states of QM can be considered as labels for Gaussian measures concentrated on one dimensional complex subspaces of phase space that are invariant with respect to the Schrödinger dynamics. “A quantum system in a stationary state ψ” in PCSFT is nothing else than a Gaussian ensemble of classical fields (fluctuations of the vacuum field of a very small magnitude) which is not changed in the process of Schrödinger's evolution. We interpret in this way the problem of stability of hydrogen atom. One of unexpected consequences of PCSFT is the infinite dimension of physical space on the prequantum scale.     

Gauge Transformations for a Family of Nonlinear Schrödinger Equations

Abstract

An enlarged gauge group acts nonlinearly on the class of nonlinear Schrödinger equations introduced by the author in joint work with Doebner. Here the equations and the group action are displayed in the presence of an external electromagnetic field. All the gauge-invariants are listed for the coupled nonlinear “Schrödinger-Maxwell” theory. Time-dependent gauge parameters result in additional terms of the type introduced by Kostin and Bialynicki-Birula and Mycielski, but Maxwell’s equations for the (non-quantized) gauge-invariant electric and magnetic fields remain linear.     

Rigorous Solutions for the One-Dimensional Hartmann Potential in the Quantum Phase-Space Representation

The rigorous solutions of the Schrödinger equation with the one-dimensional Hartmann potential for a particle are solved and discussed within the framework of the quantum phase space representation established by Torres-Vega and Frederick. For a simple example, the uncertainty principle for the quantum probability density functions is revealed in phase space representation.     

Quantum ring states in magnetic field and delayed half-cycle pulses

The present work is dedicated to the time evolution of excitation of a quantum ring in external electric and magnetic fields. Such a ring of mesoscopic dimensions in an external magnetic field is known to exhibit a wide variety of interesting physical phenomena. We have studied the dynamics of the single electron quantum ring in the presence of a static magnetic field and a combination of delayed half-cycle pulse pair. Detailed calculations have been worked out and the impact on dynamics by variation in the ring radius, intensity of external electric field, delay between the two pulses, and variation in magnetic field have been reported. A total of 19 states have been taken and the population transfer in the single electron quantum ring is studied by solving the time-dependent Schrödinger equation (TDSE), using the efficient fourth-order Runge–Kutta method. Many interesting features have been observed in the transition probabilities with the variation of magnetic field, delay between pulses and ring dimensions. A very important aspect of the present work is the persistent current generation in a quantum ring in the presence of external magnetic flux and its periodic variation with the magnetic flux, ring dimensions and pulse delay.