On a relation of the angular frequency to the Aharonov–Casher geometric phase in a quantum dot

By analysing the behaviour of a neutral particle with permanent magnetic dipole moment confined to a quantum dot in the presence of a radial electric field, Coulomb-type and linear confining potentials, then, an Aharonov–Bohm-type effect for bound states and a dependence of the angular frequency of the system on the Aharonov–Casher geometric phase and the quantum numbers associated with the radial modes, the angular momentum and the spin are obtained. In particular, the possible values of the angular frequency and the persistent spin currents associated with the ground state are investigated in two different cases.     

Extension of Haag’s theorem in the case of the lorentz invariant noncommunitative quantum field theory in a space with arbitrary dimension

The generalized Haag theorem was proven in SO(1, k) invariant quantum field theory. Apart from the k + 1 variables, an arbitrary number of additional coordinates, including noncommutative ones, can occur in the theory. In SO(1, k) invariant theory new corollaries of the generalized Haag theorem are obtained. It has been proven that the equality of four-point Wightman functions in the two theories leads to the equality of elastic scattering amplitudes and thus to the equality of the total cross sections in these theories. It was also shown that at k > 3 the equality of (k + 1) point Wightman functions in the two theories leads to the equality of the scattering amplitudes of some inelastic processes. In the SO(1, 1) invariant theory it was proven that if in one of the theories under consideration the S-matrix is equal to unity, then in another theory the S-matrix equals unity as well.     

Quantum phase distribution and the number—phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states:solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.     

On the Effect of Quantum Noise in a Quantum-Relativistic Prisoner’s Dilemma Cellular Automaton

The disrupting effect of quantum noise on the dynamics of a spatial quantum relativistic formulation of the iterated prisoner’s dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The game is assessed in fair and unfair contests.     

Quantum criticality of quantum speed limit for a two-qubit system in the spin chain with the Dzyaloshinsky–Moriya interaction

We study the quantum speed limit (QSL) time of a two-qubit system coupled to a spin–chain model with the Dzyaloshinsky–Moriya (DM) interaction. For the Bell state coupled to the Ising model or anisotropic XY model, we find that there is a prominent corresponding relationship between the QSL time and quantum phase transition in a spin–chain environment with larger scale, and the DM interaction can strongly enhance or suppress the response relation. Remarkably, when the surrounding environment is set to the XX model, the DM interaction makes it possible for us to witness the quantum phase transition by the local anomalous enhancement of the QSL time near the critical point. In addition, our analyses indicate that the entanglement can speed-up the system evolution in many-body environment.     

Dilatonic black holes in gravity’s rainbow with a nonlinear source: the effects of thermal fluctuations

This paper is devoted to an investigation of nonlinearly charged dilatonic black holes in the context of gravity’s rainbow with two cases: (1) by considering the usual entropy, (2) in the presence of first order logarithmic correction of the entropy. First, exact black hole solutions of dilatonic Born–Infeld gravity with an energy dependent Liouville-type potential are obtained. Then, thermodynamic properties of the mentioned cases are studied, separately. It will be shown that although mass, entropy and the heat capacity are modified due to the presence of a first order correction, the temperature remains independent of it. Furthermore, it will be shown that divergences of the heat capacity, hence phase transition points are also independent of a first order correction, whereas the stability conditions are highly sensitive to variation of the correction parameter. Except for the effects of a first order correction, we will also present a limit on the values of the dilatonic parameter and show that it is possible to recognize AdS and dS thermodynamical behaviors for two specific branches of the dilatonic parameter. In addition, the effects of nonlinear electromagnetic field and energy functions on the thermodynamical behavior of the solutions will be highlighted and dependency of critical behavior, on these generalizations will be investigated.     

Effect of impurity on the absorption of a parabolic quantum dot with including Rashba spin–orbit interaction

In this paper, the influence of impurity parameters on the electron energy spectrum and absorption coefficients in a parabolic quantum dot and in the presence of Rashba spin–orbit interaction subjected to a perpendicular magnetic field is studied. The impurity potential is approximated by a Gaussian form. We have shown that in the both cases of a repulsive and attractive Gaussian impurity, the absorption coefficients are strongly affected by the decay length. These coefficients show blue (red) shift as the decay length of repulsive (attractive) impurity is increased. The dependence of the absorption coefficients on the impurity position is also examined for different polarizations. Our results show that the absorption coefficient has local maximum (minimum) for a given value of impurity position for Y-polarized (X-polarized) light.     

Influence of electric field,hydrostatic pressure and temperature on the electronic states in a Pöschl-Teller quantum well

Influence of the electric field and hydrostatic pressure on the electronic states in a Pöschl-Teller quantum well is studied. In the framework of variational method the dependences of the ground state energy on the electric field and hydrostatic pressure are calculated for different values of the potential parameters and the temperature. It is shown that the increase in the electric field leads to the increase in the ground state energy, while the increase in the well width leads to the strengthening of the electric field effect. The ground state energy decreases with increasing pressure and increases with increasing temperature.     

“Soft” modes of the excitation spectrum constructed on perturbations of the Abrikosov lattice with a single flux quantum in the unit cell

We have analyzed the spectrum of gapless excitations emerging upon the perturbation of the Abrikosov lattice with a single flux quantum in the unit cell. Superconductors with Ginzburg–Landau parameter κ close to unity are of special interest. We have determined the spectrum of gapless excitations close to zeroth shear modes for an arbitrary angle ? between the unit cell vectors. Analysis of the excitation spectra of triangular and square lattices with a single flux quantum in the unit cell has shown that solutions with a number of flux quanta greater than one exist at least in the range of parameters κ close to unity (κ > 1) and give smaller values of the free energy as compared to its values for a triangular lattice with a single flux quantum. For small values of momentum k (in the k ² approximation), the excitation spectrum of the “transverse” mode in the triangular lattice is independent of the direction of the momentum lying in the plane perpendicular to the magnetic field. For the square lattice (? = π/2), the transverse mode is anisotropic in the k ² approximation also.     

Spectral and Quantum‐Chemical Investigation of the Influence of the Spatial Structure of a Polymeric Complex on the Mechanism of Catalytic Oxidation of Sulfur Dioxide with Oxygen

Based on the calculations carried out by the ZINDO/S method, we suggest interpretation of the electronic absorption spectra of solvate complexes of cobalt with polyethyleneimine and sulfite ion. The quantumchemical analysis of the spectrophotometric data has shown that the change in a concentration of cobalt ions in a solution leads to conformation changes in a polymeric chain. The kinetic and quantumchemical investigation of the mechanism of catalytic oxidation of SO₃ ^2– to SO₄ ^2– is carried out. We suggest a spatial structure of the transient state that provides optimum conditions for the oxygenation reaction. The kinetic data indicate that the catalytic activity of cobalt ions fixed on a polymeric matrix is by three orders of magnitude higher than of their monomeric analogs. Using calculations performed by the RM3 method, we show that the oxygenation process is of exothermal nature and that there is a direct correlation between the reactionrate constant and the energy released in the process of oxygenation (E). On substituting ammonia molecules by a polyethyleneimine fragment, E increases by 39.39 kcal/mole.     

On the Solutions of the Yang-Baxter Equations with General Inhomogeneous Eight-Vertex R-Matrix: Relations with Zamolodchikov’s Tetrahedral Algebra

We present most general one-parametric solutions of the Yang-Baxter equations (YBE) for one spectral parameter dependent R _ij (u)-matrices of the six- and eight-vertex models, where the only constraint is the particle number conservation by mod(2). A complete classification of the solutions is performed. We have obtained also two spectral parameter dependent particular solutions R _ij (u,v) of YBE. The application of the non-homogeneous solutions to construction of Zamolodchikov’s tetrahedral algebra is discussed.     

Effect of electric field on the spectrum and the persistent current of a quantum ring with two electrons （II） additional effect of a charged impurity

This paper studies the effect of a charged impurity together with or without an external homogeneous electric field on a quantum ring threaded by a magnetic field B and containing two electrons. The potential caused by the impurity has been plotted which is helpful to the understanding of the electronic structures inside the ring. The deep valley appearing in the potential curve is the source of localization, which affects seriously the Aharonov-Bohm oscillation （ABO） of the energy and persistent current. It also causes the fluctuation of the total orbital angular momentum L of the pair of electrons. It is found that the appearance of the impurity reduces the domain of the fractional ABO. During the increase of B, the domain of the integral ABO may appear earlier when B is even quite small. The transition from the localized states to extended states has also been studied. Furthermore, it has deduced a set of related formulae for a transformation, by which an impurity with a charge ep placed at an arbitrary point Rp is equivalent to an impurity with a revised charge ep placed at the X-axis with a revised radial distance Rp. This transformation facilitates the calculation and make the analysis of the physical result clearer.     

Differential-geometric structures associated with the Lagrangian and a nonvariational interpretation of the Euler equations and Nöther’s theorem

Differential-geometry structures associated with Lagrangians are studied. A relative invariant E embraced by an extension of fundamental object is constructed (in the paper, E is referred to as the Euler relative invariant) such that the equation E = 0 is an invariant representation of the Euler equation for the variational functional. For this reason, a nonvariational interpretation of the Euler equations becomes possible, because the Euler equations need not be connected with the variational problem, and one can regard the equations from the very beginning as an equation arising when equating the Euler relative invariant to zero. Local diffeomorphisms between two structures associated with Lagrangians are also discussed. The theorem concerning conditions under which the vanishing condition for the Euler relative invariant of one of these structures leads to vanishing of the Euler invariant relative of the other structure can be treated as a nonvariational interpretation of Nöther’s theorem.     

Playing with Quantum Toys: Julian Schwinger’s Measurement Algebra and the Material Culture of Quantum Mechanics Pedagogy at Harvard in the 1960s

In the early 1960s, a PhD student in physics, Costas Papaliolios, designed a simple—and playful—system of Polaroid polarizer filters with a specific goal in mind: explaining the core principles behind Julian Schwinger’s quantum mechanical measurement algebra, developed at Harvard in the late 1940s and based on the Stern-Gerlach experiment confirming the quantization of electron spin. Papaliolios dubbed his invention “quantum toys.” This article looks at the origins and function of this amusing pedagogical device, which landed half a century later in the Collection of Historical Scientific Instruments at Harvard University. Rendering the abstract tangible was one of Papaliolios’s demonstration tactics in reforming basic teaching of quantum mechanics. This article contends that Papaliolios’s motivation in creating the quantum toys came from a renowned endeavor aimed, inter alia, at reforming high-school physics training in the United States: Harvard Project Physics. The pedagogical study of these quantum toys, finally, compels us to revisit the central role playful discovery performs in pedagogy, at all levels of training and in all fields of knowledge.     

Arnol’d diffusion in a system with 2.5 degrees of freedom: Classical and quantum mechanical approaches

Arnol’d diffusion, a universal phenomenon in nonlinear dynamics, is analyzed for a model system with 2.5 degrees of freedom. Only the three primary order resonances are taken into account, and the results obtained by using classical and quantum mechanical approaches are compared. It is shown that the parameter dependence of the rate of quantum Arnol’d diffusion is similar to the classical one, but the quantum diffusion coefficient is smaller by approximately an order of magnitude. It is found that the existence of a threshold with respect to perturbation parameters, pointed out earlier, is not an indispensable feature of quantum Arnol’d diffusion. It is shown that a quantum system with weakly overlapping resonances can exhibit mixed dynamics that has no classical counterpart (diffusion along a resonance superimposed by oscillations across the overlapped resonances).     

A hopf star-algebra of polynomials on the quantum SL(2, ℝ) for a ‘unitary’ R-matrix

A Hopf *-algebra corresponding to a solution of the classical Yang-Baxter equation is introduced, providing a new quantum deformation of SL (2 ).     

On the Violation of Ohm’s Law for Bounded Interactions: a One Dimensional System

We consider an infinite Hamiltonian system in one space dimension, given by a charged particle subjected to a constant electric field and interacting with an infinitely extended system of particles. We discuss conditions on the particle/medium interaction which are necessary for the charged particle to reach a finite limiting velocity. We assume that the background system is initially in an equilibrium Gibbs state and we prove that for bounded interactions the average velocity of the charged particle increases linearly in time. This statement holds for any positive intensity of the electric field, thus contradicting Ohms law.Work partially supported by the GNFM-INDAM and the Italian Ministry of the University.