General Approach to the Quantum Kicked Particle in a Magnetic Field: Quantum-Antiresonance Transition

The quantum kicked particle in a magnetic field is studied in a weak-chaos regime under realistic conditions, i.e., for {\em general} values of the conserved coordinate $x_{{\rm c}}$ of the cyclotron orbit center. The system exhibits spectral structures [``Hofstadter butterflies'' (HBs)] and quantum diffusion depending sensitively on $x_{{\rm c}}$. Most significant changes take place when $x_{{\rm c}}$ approaches the value at which quantum antiresonance (exactly periodic recurrences) can occur: the HB essentially ``doubles'' and the quantum-diffusion coefficient $D(x_{{\rm c}})$ is strongly reduced. An explanation of these phenomena, including an approximate formula for $D(x_{{\rm c}})$ in a class of wave packets, is given on the basis of an effective Hamiltonian which is derived as a power expansion in a small parameter. The global quantum diffusion of a two-dimensional wave packet for all $x_{{\rm c}}$ is briefly considered.Comment: Revised Version, publishe

General approach to potentials with two known levels

We present the general form of potentials with two given energy levels $E_{1}$, $E_{2}$ and find corresponding wave functions. These entities are expressed in terms of one function $\xi (x)$ and one parameter $\Delta E=E_{2}$-$E_{1}$. We show how the quantum numbers of both levels depend on properties of the function $\xi (x)$. Our approach does not need resorting to the technique of supersymmetric (SUSY) quantum mechanics but automatically generates both the potential and superpotential.Comment: 14 pages, REVTeX 3.0. In v.2 misprints and inaccuracies in presentation corrected, discussion of 3-dim. case added. In v.3 misprint in eq. 41, several typos and inaccuracies in English corrected. To be published in J. of Phys. A: Math. Ge

Quasi-exactly solvable quartic Bose Hamiltonians

We consider Hamiltonians, which are even polynomials of the forth order with the respect to Bose operators. We find subspaces, preserved by the action of Hamiltonian These subspaces, being finite-dimensional, include, nonetheless, states with an \QTR{it}{infinite} number of quasi-particles, corresponding to the original Bose operators. The basis functions look rather simple in the coherent state representation and are expressed in terms of the degenerate hypergeometric function with respect to the complex variable labeling the representation. In some particular degenerate cases they turn (up to the power factor) into the trigonometric or hyperbolic functions, Bessel functions or combinations of the exponent and Hermit polynomials. We find explicitly the relationship between coefficients at different powers of Bose operators that ensure quasi-exact solvability of Hamiltonian.Comment: 21 pages, REVTeX 3.0, no figures. In v.2 couple of misprints in English corrected. To be published in J. Phys. A: Math. Ge

Coherent Acceleration of Material Wavepackets

We study the quantum dynamics of a material wavepacket bouncing off a modulated atomic mirror in the presence of a gravitational field. We find the occurrence of coherent accelerated dynamics for atoms. The acceleration takes place for certain initial phase space data and within specific windows of modulation strengths. The realization of the proposed acceleration scheme is within the range of present day experimental possibilities.Comment: 6 pages, 3 figures, NASA "Quantum-to-Cosmos" conference proceedings to be published in IJMP

Modelling by maps of two-frequency microwave ionization of hydrogen atoms

Mapping equations of motion of the highly exited classical atom in a monochromatic field are generalized for the two-frequency microwave field. Analysis of the obtained equations indicates to the weak sensitivity of the position of the recently observed ionization peak near the main resonance to the frequency and amplitude of the additional microwave field. In the high frequency region, however, the sensitivity of the enhanced ionization peaks on the additional field frequency is predicted.Comment: LaTex, 3 PostScript figure

Near-extremal and extremal quantum-corrected two-dimensional charged black holes

We consider charged black holes within dilaton gravity with exponential-linear dependence of action coefficients on dilaton and minimal coupling to quantum scalar fields. This includes, in particular, CGHS and RST black holes in the uncharged limit. For non-extremal configuration quantum correction to the total mass, Hawking temperature, electric potential and metric are found explicitly and shown to obey the first generalized law. We also demonstrate that quantum-corrected extremal black holes in these theories do exist and correspond to the classically forbidden region of parameters in the sense that the total mass $M_{tot}<Q$ ($Q$ is a charge). We show that in the limit $T_{H}\to 0$ (where $T_{H}$ is the Hawking temperature) the mass and geometry of non-extremal configuration go smoothly to those of the extremal one, except from the narrow near-horizon region. In the vicinity of the horizon the quantum-corrected geometry (however small quantum the coupling parameter $\kappa$ would be) of a non-extremal configuration tends to not the quantum-corrected extremal one but to the special branch of solutions with the constant dilaton (2D analog of the Bertotti-Robinson metric) instead. Meanwhile, if $\kappa =0$ exactly, the near-extremal configuration tends to the extremal one. We also consider the dilaton theory which corresponds classically to the spherically-symmetrical reduction from 4D case and show that for the quantum-corrected extremal black hole $M_{tot}>Q$.Comment: 25 pages. Typos corrected. To appear in Class. Quant. Gra

Entropy of Quantum Fields for Nonextreme Black Holes in the Extreme Limit

Nonextreme black hole in a cavity within the framework of the canonical or grand canonical ensemble can approach the extreme limit with a finite temperature measured on a boundary located at a finite proper distance from the horizon. In spite of this finite temperature, it is shown that the one-loop contribution $S_{q\text{ }}$of quantum fields to the thermodynamic entropy due to equilibrium Hawking radiation vanishes in the limit under consideration. The same is true for the finite temperature version of the Bertotti-Robinson spacetime into which a classical Reissner-Nordstr\"{o}m black hole turns in the extreme limit. The result $S_{q}=0$ is attributed to the nature of a horizon for the Bertotti-Robinson spacetime.Comment: 11 pages, ReVTeX, no figures. New references added, discussion expanded, presentation and English improved. Accepted for publication in Phys. Rev.

Phase transition between quantum and classical regimes for the escape rate of a biaxial spin system

Employing the method of mapping the spin problem onto a particle one, we have derived the particle Hamiltonian for a biaxial spin system with a transverse or longitudinal magnetic field. Using the Hamiltonian and introducing the parameter $p (\equiv (U_{max}-E)/(U_{max}-U_{min}))$ where $U_{max}$ (U_{min}) corresponds to the top (bottom) of the potential and $E$ is the energy of the particle, we have studied the first- or second-order transition around the crossover temperature between thermal and quantum regimes for the escape rate, depending on the anisotropy constant and the external magnetic field. It is shown that the phase boundary separating the first- and second-order transition and its crossover temperature are greatly influenced by the transverse anisotropy constant as well as the transverse or longitudinal magnetic field.Comment: 5 pages + 3 figures, to be published in Phys. Rev.

Coherent acceleration of material wavepackets in modulated optical fields

We study the quantum dynamics of a material wavepacket bouncing off a modulated atomic mirror in the presence of a gravitational field. We find the occurrence of coherent accelerated dynamics for atoms beyond the familiar regime of dynamical localization. The acceleration takes place for certain initial phase space data and within specific windows of modulation strengths. The realization of the proposed acceleration scheme is within the range of present day experimental possibilities

Extremal limit of the regular charged black holes in nonlinear electrodynamics

The near horizon limit of the extreme nonlinear black hole is investigated. It is shown that resulting geometry belongs to the AdS2xS2 class with different modules of curvatures of subspaces and could be described in terms of the Lambert functions. It is demonstrated that the considered class of Lagrangians does not admit solutions of the Bertotti-Robinson type