Zero-energy bound states in superconductor/ferromagnet superlattices

Andreev bound states in monoatomic superconductor–ferromagnet (S/F) superlattices are studied theoretically, assuming tunneling between S and F layers in perpendicular direction. Andreev reflection at S/F interfaces is strongly affected by the exchange interaction h in F layers. In the ground state, only for h≠0 zero-energy states (ZES) are formed on S and F layers. For h=0, corresponding to superconductor–normal metal (S/N) superlattices, ZES may appear in the nonequilibrium phase, =π. This is found both for s-wave and d-wave symmetry of the order parameter in S. The conditions for ZES are obtained as a function of h, of the transfer integral t for movement of quasiparticles (QPs) between S and F layers, and of the corresponding ground state phase difference _eq between two neighboring S layers.     

Computation of bound states for 2D potentials using discrete basis

Using a suitable Laguerre basis set that ensures a tridiagonal matrix representation of the reference Hamiltonian, we were able to evaluate in closed form the matrix representation of the associated Hamiltonian for two exactly solvable 2D potentials. This enabled us to treat analytically the full Hamiltonian and compute the associated bound states spectrum as the eigenvalues of the associated analytical matrix representing their Hamiltonians. Finally we compared our results satisfactorily with those obtained using the Gauss quadrature numerical integration approach.

PACS numbers: 03.65.Ge, 34.20.Cf, 03.65.Nk, 34.20.Gj     

库仑势加新环形势的相对论束缚态

在标量势等于矢量势的条件下，获得了库仑势加新环形势的Klein-Gordon方程和Dirac方程的束缚态的精确解. 对于Klein-Gordon方程，获得了精确的能谱方程和归一化的波函数. 对于Dirac方程，给出了精确的能谱方程和归一化的旋量波函数. 关键词： 库仑势加新环形势 束缚态 精确解     

Exact, zero-energy, square-integrable solutions of a model related to the Maxwell’s fish-eye problem

A model, which admits normalizable wave functions of the Schrödinger equation at the energy of E = 0, is exactly solved and the solutions are compared to the corresponding classical trajectories. The wave functions are proved to be square-integrable for discrete (quantized) values of the coupling constant of the used potential. We also show that our model is a specific version of the well-known Maxwell’s fish-eye. This is performed with the help of a suitably chosen conformal mapping.     

Objective uncertainty relation with classical background in a statistical model

We show within a statistical model of quantization reported in the previous work based on Hamilton–Jacobi theory with a random constraint that the statistics of fluctuations of the actual trajectories around the classical trajectories in velocity and position spaces satisfy a reciprocal uncertainty relation. The relation is objective (observation independent) and implies the standard quantum mechanical uncertainty relation.     

Decoherence of odd compass states in the phase-sensitive amplifying/dissipating environment

We study the evolution of odd compass states (specific superpositions of four coherent states), governed by the standard master equation with phase-sensitive amplifying/attenuating terms, in the presence of a Hamiltonian describing a parametric degenerate linear amplifier. Explicit expressions for the time-dependent Wigner function are obtained. The time of disappearance of the so called “sub-Planck structures” is calculated using the negative value of the Wigner function at the origin of phase space. It is shown that this value rapidly decreases during a short “conventional interference degradation time” (CIDT), which is inversely proportional to the size of quantum superposition, provided the anti-Hermitian terms in the master equation are of the same order (or stronger) as the Hermitian ones (governing the parametric amplification). The CIDT is compared with the final positivization time (FPT), when the Wigner function becomes positive. It appears that the FPT does not depend on the size of superpositions, moreover, it can be much bigger in the amplifying media than in the attenuating ones. Paradoxically, strengthening the Hamiltonian part results in decreasing the CIDT, so that the CIDT almost does not depend on the size of superpositions in the asymptotical case of very weak reservoir coupling. We also analyze the evolution of the Mandel factor, showing that for some sets of parameters this factor remains significantly negative, even when the Wigner function becomes positive.     

A note on the asymptotic master equations for systems with bound states

It is shown that, within the convolutionless formalism of Fuliski, the asymptotic form (in time) of the Liouville equation does not change with the existence of bound states in the energy spectrum of the system under consideration.     

Particle-hole bound states of dipolar molecules in an optical lattice

We investigate the particle-hole pair excitations of dipolar molecules in an optical lattice, which can be described with an extended Bose-Hubbard model. For strong enough dipole-dipole interaction, the particle-hole pair excitations can form bound states in one and two dimensions. With decreasing dipole-dipole interaction, the energies of the bound states increase and merge into the particle-hole continuous spectrum gradually. The existence regions, the energy spectra and the wave functions of the bound states are carefully studied and the symmetries of the bound states are analyzed with group theory. For a given dipole-dipole interaction, the number of bound states varies in momentum space and a number distribution of the bound states is illustrated. We also discuss how to observe these bound states in future experiments.     

二维环状δ势的束缚态

讨论了二维自由空间和各向同性谐振子势下环状δ势束缚态波函数的表示,发现波函数由合流超几何函数和屈科米函数表示.由波函数在边界的衔接条件,得到了能谱方程,并给出了一定条件下前5个能级的数值解.     

Bound states of Klein—Gordon equation for double ring-shaped oscillator scalar and vector potentials

In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for θ and r coordinates. Exact bound state solutions of Klein—Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.     

Quantum–classical correspondence and the role of the dipole function in molecular dissociation

We consider the quantum and classical dissociation dynamics of heteronuclear diatomic molecules induced by infrared laser pulses. The field–molecule interaction is given by the product of the time-dependent electric field and the molecule permanent dipole. We investigate the influence of the dipole function in molecular dissociation. We show that the dissociation can be suppressed at certain external field frequencies for a nonlinear and finite-range dipole function. The correspondence between quantum and classical results is established by relating classical Fourier amplitudes to discrete–continuum quantum matrix elements.     

Two-phonon bound states in imperfect crystals

The question of the occurrence of two-phonon bound states in imperfect crystals is investigated. It is shown that the anharmonicity mediated two-phonon bound state which is present in perfect crystals gets modified due to the presence of impurities. Moreover, the possibility of the occurrence of a purely impurity mediated two-phonon bound state is demonstrated. The bound state frequencies are calculated using the simple Einstein oscillator model for the host phonons. The two-phonon density of states for the imperfect crystal thus obtained has peaks at the combination and difference frequencies of two host phonons besides the peaks at the bound state frequencies. For a perfect crystal the theory predicts a single peak at the two-phonon bound state frequency in conformity with experimental observations and other theoretical calculations. Experimental data on the two-phonon infrared absorption and Raman scattering from mixed crystals of GA_1−c Al _c P and Ge_1−c Si _c are analysed to provide evidence in support of impurity-mediated two-phonon bound states. The relevance of the zero frequency (difference spectrum) peak to the central peak observed in structural phase transitions, is conjectured; This work is a part of the thesis to be submitted by one of the authors (SS) in partial fulfilment of the degree of Doctor of Philosophy to Utkal University, Bhubaneswar, India.     

Two-vibron bound states in the β--Fermi--Pasta--Ulam model

This paper studies the two-vibron bound states in the β- Fermi Pasta-Ulam model by means of the number conserving approximation combined with the number state method. The results indicate that on-site, adjacent-site and mixed two-vibron bound states may exist in the model. Specially, wave number has a significant effect on such bound states, which may be considered as the quantum effects of the localized states in quantum systems.     

Non-threshold (F, Dp) bound states

In the previous paper [hep-th/9904112], we argued that there exist BPS bound states of Dp branes carrying certain units of quantized constant electric field for every p (with 1 p 8). Each of these bound states preserves one half of the spacetime supersymmetries. In this paper, we construct these bound state configurations explicitly for 2 p 7 from Schwarz's (m, n)-string or (F, D1) bound state in type IIB string theory by T-dualities along the transverse directions. We calculate the charge per of (p − 1)-dimensional area for F-strings in (F,Dp) and the tension for each of these bound states. The results agree precisely with those obtained previously from the worldvolume study. We study the decoupling limit for the (F, D3) bound state and find that Maldacena's AdS₅/CFT₄ correspondence may hold true even with respect to this bound state but now with an effective string coupling rather than the usual string coupling. This coupling is quantized and can be independent of the usual string coupling in a certain limit.     

Study of theS-matrix near bound states in the continuum

The behaviour ofS-matrix for potentials generating bound states in continuum in the neighbourhood of the positive bound state energies is studied. It is shown that unlike the case of usual negative energy bound states, theS-matrix does not have a pole at the positive bound state energy but becomes unity at the energy corresponding to bound states in continuum. Calculations ofS-waveS-matrix for a local potential constructed by Stillinger and Herrick and a separable nonlocal potential constructed by the present authors verify these results. Our results indicate that the bound states embedded in continuum constructedvia the von Neumann and Wigner procedure cannot be interpreted as resonances with zero width.     

Kinetic equations for a quantum gas with bound states

The kinetic theory for dense gases is modified to take into account the existence of bound states. A molecular chaos condition is used which corresponds to the division of the two- and three-particle Hubert spaces into scattering and boundstate subspaces. A kinetic stage results from a long-time limit which converges to yield time-independent functionals for the two- and three-particle density matrices, as functionals of the density matrices for atoms and molecules. Coupled kinetic equations are obtained which describe the gas as a reacting mixture of atoms and diatomic molecules. These include the effects of scattering and rearrangement collisions between the atom and the molecule, and of molecular formation and dissociation.     

Effective Hamiltonian for bound states in Yukawa theory

A generalization of the Gell-Mann–Low theorem is applied to lowest nontrivial order to determine an effective Hamiltonian for two-fermion states in relativistic Yukawa theory. The consistency of the corresponding effective Schrödinger equation is thoroughly investigated in various aspects, among others the nonrelativistic and one-body limits, and the small-distance or large-momentum regime of the bound state solutions is discussed in detail.     

环形非球谐振子势Klein-Gordon方程的束缚态

用分离变量方法讨论了在环形非球谐振子标量势和矢量势相等条件下的Klein-Gordon方程的束缚态解.给出了用广义连带勒让得多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数，获得了精确的束缚态能谱方程. 关键词： 环形非球谐振子势 Klein-Gordon方程 束缚态     

Suppression of leakage effect of Majorana bound states in the T-shaped quantum-dot structure

We theoretically study the transport properties in the T-shaped double-quantum-dot structure, by considering the dot in the main channel to be coupled to the Majorana bound state(MBS) at one end of the topological superconducting nanowire.It is found that the side-coupled dot governs the effect of the MBS on the transport behavior. When its level is consistent with the energy zero point, the MBS contributes little to the conductance spectrum. Otherwise, the linear conductance exhibits notable changes according to the inter-MBS coupling manners. In the absence of inter-MBS coupling, the linear conductance value keeps equal to e~2/2 h when the level of the side-coupled dot departs from the energy zero point. However,the linear conductance is always analogous to the MBS-absent case once the inter-MBS coupling comes into play. These findings provide new information about the leakage effect of MBSs in quantum-dot structures.