Quasiclassical Region Research Articles

On the creation of charged massless fermion pair by a photon in an external constant uniform magnetic field in 2+1 dimensions

Creation of charged massless fermion pair by a photon in a constant uniform magnetic field is considered in the one-loop approximation of the [Formula: see text]-dimensional quantum electrodynamics (QED[Formula: see text]). We calculate the elastic scattering amplitude (EAS) of photon using the polarization operator of photon in the above magnetic field obtained earlier in our work. We analyze the elastic scattering amplitude of photon at various values of the photon energy and magnetic field strength. Very simple analytical formulas for EAS of photon are obtained in the so-called quasi-classical region. In the massive quantum electrodynamics the elastic scattering amplitude of photon defines its “mass” squared in the presence of external electromagnetic field and the imaginary part of EAS describes the total probability of charged massive fermion pair creation in the electromagnetic field; we assume that it is the case and in the massless quantum electrodynamics.

Structure of the channeling electrons wave functions under dynamical chaos conditions

The stationary wave functions of fast electrons axially channeling in the silicon crystal near [110] direction have been found numerically for integrable and non-integrable cases, for which the classical motion is regular and chaotic, respectively. The nodal structure of the wave functions in the quasi-classical region, where the energy levels density is high, is agreed with quantum chaos theory predictions.

On the statistical properties of energy levels in quantum theory of axial channeling

The energy levels of electrons moving in the mode of axial channeling in a system of parallel chains of atoms (chains of the Si[110] crystal are used as an example) are found numerically in this paper. The obtained distributions of intervals between neighboring energy levels in the quasiclassical region are compared with predictions for systems demonstrating regular and chaotic behavior at the classical limit.

Universal local pair correlations of Lieb-Liniger bosons at quantum criticality

The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ in the quantum critical regime, the TLL phase and the quasi-classical region, where $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon=\frac{\hbar^2}{2m} c^2$ with interaction strength $c$ and linear density $n$. This suggests the possibility to test finite temperature local pair correlations for the TLL in the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation.

Quantum dynamical effects as a singular perturbation for observables in open quasi-classical nonlinear mesoscopic systems

We review our results on a mathematical dynamical theory for observables for open many-body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian provide a singular “quantum” perturbation for observables in some “mesoscopic” region of parameters. In particular, quantum effects result in secular terms in the dynamical evolution, that grow in time. We argue that even for open quantum nonlinear systems in the deep quasi-classical region, these quantum effects can survive after decoherence and relaxation processes take place. We demonstrate that these quantum effects in open quantum systems can be observed, for example, in the frequency Fourier spectrum of the dynamical observables, or in the corresponding spectral density of noise. Estimates are presented for Bose–Einstein condensates, low temperature mechanical resonators, and nonlinear optical systems prepared in large amplitude coherent states. In particular, we show that for Bose–Einstein condensate systems the characteristic time of deviation of quantum dynamics for observables from the corresponding classical dynamics coincides with the characteristic time-scale of the well-known quantum nonlinear effect of phase diffusion.

The Big-Bang singularity in the framework of a Generalized Uncertainty Principle

We analyze the quantum dynamics of the Friedmann–Robertson–Walker Universe in the context of a Generalized Uncertainty Principle. Since the isotropic Universe dynamics resembles that of a one-dimensional particle, we quantize it with the commutation relations associated to an extended formulation of the Heisenberg algebra. The evolution of the system is described in terms of a massless scalar field taken as a relational time. We construct suitable wave packets and analyze their dynamics from a quasi-classical region to the initial singularity. The appearance of a non-singular dynamics comes out as far as the behavior of the probability density is investigated. Furthermore, reliable indications arise about the absence of a big-bounce, as predicted in recent issues of loop quantum cosmology.

Survival of quantum effects for observables after decoherence

When a quantum nonlinear system is linearly coupled to an infinite bath of harmonic oscillators, quantum coherence of the system is lost on a decoherence time scale ${\ensuremath{\tau}}_{D}$. Nevertheless, quantum effects for observables may still survive environment-induced decoherence and be observed for times much larger than the decoherence time scale. In particular, we show that the Ehrenfest time, which characterizes a departure of quantum dynamics for observables from the corresponding classical dynamics, can be observed for a quasiclassical nonlinear oscillator for times $\ensuremath{\tau}⪢{\ensuremath{\tau}}_{D}$. We discuss this observation in relation to recent experiments on quantum nonlinear systems in the quasiclassical region of parameters.

Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology

We solve the Wheeler-DeWitt equation for the minisuperspace of a cosmological Bianchi type-I model with a minimally coupled massive scalar field $\ensuremath{\varphi}$ as the source by generalizing the calculation of Lukash and Schmidt [Astron. Nachr. 309, 25 (1988)]. Contrary to other approaches we allow strong anisotropy. Combining analytical and numerical methods, we apply an adiabatic approximation for $\ensuremath{\varphi},$ and as a new feature we find a period-doubling bifurcation. This bifurcation takes place near the cosmological quantum boundary, i.e., the boundary of the quasiclassical region with an oscillating $\ensuremath{\psi}$ function where the WKB approximation is good. The numerical calculations suggest that such a notion of a ``cosmological quantum boundary'' is well defined, because, sharply beyond that boundary, the WKB approximation is no longer applicable at all. This result confirms the adequateness of the introduction of a cosmological quantum boundary in quantum cosmology.

New Padé approximations for the free charges in two-component strongly coupled plasmas based on the Unsöld-Berlin-Montroll asymptotics

Based on the available analytical formulae for the physical properties of the free charges in the quasi-classical density-temperature region new Padé approximations are derived. In the quasi-classical region the thermodynamical functions are at strong coupling determined by a linear dependence on the Γ-parameter, similar as for the strongly coupled electron gas. The existing Padé approximations for strongly coupled plasmas are modified in such a way that in the quasi-classical region the correct asymptotics is obtained. Based on the slope predicted by the Unsöld theory, by the Berlin-Montroll theory or corresponding theories with linear Γ asymptotics including corrections, concrete expressions are obtained and compared with other analytical approaches that neglect this case of asymptotics.

Relativistic Semiclassical Wave Equation and its Solution

The properties of relativistic particles in the quasiclassical region are investigated. The relativistic semiclassical wave equation appropriate in the quasiclassical region is derived. It is shown that the leading-order WKB quantization rule is the appropriate method to solve the equation obtained.

Quantum versus classical decay laws in open chaotic systems

We study analytically the time evolution in decaying chaotic systems and discuss in detail the hierarchy of characteristic time scales that appeared in the quasiclassical region. There exist two quantum time scales: the Heisenberg time t_H and the time t_q=t_H/\sqrt{\kappa T} (with \kappa >> 1 and T being the degree of resonance overlapping and the transmission coefficient respectively) associated with the decay. If t_q < t_H the quantum deviation from the classical decay law starts at the time t_q and are due to the openness of the system. Under the opposite condition quantum effects in intrinsic evolution begin to influence the decay at the time t_H. In this case we establish the connection between quantities which describe the time evolution in an open system and their closed counterparts.

Semiclassical wave equation and exactness of the WKB method.

The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB quantization condition to this equation reproduces exact energy eigenvalues for all solvable spherically symmetric potentials. \textcopyright{} 1996 The American Physical Society.

Representations of quantum affine algebras

Let @ be a finite dimensional simple Lie algebra and @ the corresponding affine Kac-Moody algebra. The notion of the fusion in the category (9 of representations of a n n e Kac-Moody algebras (5 was introduced ten years ago by physicists in the framework of Conformal Field Theory. This notion was developed in a number of mathematical papers (see, for example, [TUY]) where the notion of fusion is rigorously defined and in [D1] where the relation between the fusion and quantum groups in the quasi-classical region was established. This line of development was extended in [KL] to a construction on equivalence between the "fusion" category for an arbitrary negative charge and the category of representations of the corresponding quantum group (for simply-laced affine Kac-Moody algebras).

Energy levels of a piecewise linear oscillator with a barrier

We study the spectrum of a piecewise linear one-dimensional oscillator with a δ-function barrier. The spectrum outside the quasiclassical region is highly influenced by the nature of the ratio ω 1 ω 2 , ω i being the frequencies in the linear domains of t oscillator.

Quantum mappings and the problem of stochasticity in quantum systems

Discrete mappings for a dynamical quantum system possessing in the classical limit ( ħ = 0) the property of stochasticity are analysed. The quasiclassical approximation is shown to be valid for the limited time and the asymptotic behaviour of the system for large times is to be determined by the quantum effects essentially. Contrary to the classical case when the correlation function decreases exponentially, the correlations decay with a powerlaw in the quantum case. This results in zero entropy of the quantum dynamical system while the entropy is nonzero in the classical limit case. It is shown that there is a quasiclassical region in which the quantum system dynamics is close to the stochastic dynamics of the corresponding classical system for a finite time. The parameter separating this quasiclassical region from the region of essentially quantum dynamics is obtained.