Violation of the zeroth law of thermodynamics for a non-ergodic interaction

The phenomenon described by our title should surprise no one. What may be surprising though is how easy it is to produce a quantum system with this feature; moreover, that system is one that is often used for the purpose of showing how systems equilibrate. The violation can be variously manifested. In our detailed example, bringing a detuned 2-level system into contact with a monochromatic reservoir does not cause it to relax to the reservoir temperature; rather, the system acquires the reservoir's level-occupation-ratio

Nexus between quantum criticality and the chemical potential pinning in high-TcT_c cuprates

For strongly correlated electrons the relation between total number of charge carriers $n_e$ and the chemical potential $\mu$ reveals for large Coulomb energy the apparently paradoxical pinning of $\mu$ within the Mott gap, as observed in high-$T_c$ cuprates. By unravelling consequences of the non-trivial topology of the charge gauge U(1) group and the associated ground state degeneracy we found a close kinship between the pinning of $\mu$ and the zero-temperature divergence of the charge compressibility $\kappa\sim\partial n_e/\partial\mu$, which marks a novel quantum criticality governed by topological charges rather than Landau principle of the symmetry breaking.Comment: 4+ pages, 2 figures, typos corrected, version as publishe

Topological quenching of the tunnel splitting for a particle in a double-well potential on a planar loop

The motion of a particle along a one-dimensional closed curve in a plane is considered. The only restriction on the shape of the loop is that it must be invariant under a twofold rotation about an axis perpendicular to the plane of motion. Along the curve a symmetric double-well potential is present leading to a twofold degeneracy of the classical ground state. In quantum mechanics, this degeneracy is lifted: the energies of the ground state and the first excited state are separated from each other by a slight difference ¿E, the tunnel splitting. Although a magnetic field perpendicular to the plane of the loop does not influence the classical motion of the charged particle, the quantum-mechanical separation of levels turns out to be a function of its strength B. The dependence of ¿E on the field B is oscillatory: for specific discrete values Bn the splitting drops to zero, indicating a twofold degeneracy of the ground state. This result is obtained within the path-integral formulation of quantum mechanics; in particular, the semiclassical instanton method is used. The origin of the quenched splitting is intuitively obvious: it is due to the fact that the configuration space of the system is not simply connected, thus allowing for destructive interference of quantum-mechanical amplitudes. From an abstract point of view this phenomenon can be traced back to the existence of a topological term in the Lagrangian and a nonsimply connected configuration space. In principle, it should be possible to observe the splitting in appropriately fabricated mesoscopic rings consisting of normally conducting metal

On the Origin of the -4.4 eV Band in CdTe(100)"

We calculate the bulk- (infinite system), (100)-bulk-projected- and (100)-Surface-projected Green's functions using the Surface Green's Function Matching method (SGFM) and an empirical tight-binding hamiltonian with tight-binding parameters (TBP) that describe well the bulk band structure of CdTe. In particular, we analyze the band (B--4) arising at --4.4 eV from the top of the valence band at $\Gamma$ according to the results of Niles and H\"ochst and at -4.6 eV according to Gawlik {\it et al.} both obtained by Angle-resolved photoelectron spectroscopy (ARPES). We give the first theoretical description of this band.Comment: 17 pages, Rev-TEX, CIEA-Phys. 02/9

Rotational Symmetry of Classical Orbits, Arbitrary Quantization of Angular Momentum and the Role of Gauge Field in Two-Dimensional Space

We study the quantum-classical correspondence in terms of coherent wave functions of a charged particle in two-dimensional central-scalar-potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level-space of angular momentum being greater or less than $\hbar$ is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily $2\pi$-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The quantum mechanical model of anyon proposed by Wilczek (Phys. Rev. Lette. 48, 1144) becomes a special case of the arbitrary-quantization.Comment: 6 pages, 5 figure

Propagation of charged particle waves in a uniform magnetic field

This paper considers the probability density and current distributions generated by a point-like, isotropic source of monoenergetic charges embedded into a uniform magnetic field environment. Electron sources of this kind have been realized in recent photodetachment microscopy experiments. Unlike the total photocurrent cross section, which is largely understood, the spatial profiles of charge and current emitted by the source display an unexpected hierarchy of complex patterns, even though the distributions, apart from scaling, depend only on a single physical parameter. We examine the electron dynamics both by solving the quantum problem, i. e., finding the energy Green function, and from a semiclassical perspective based on the simple cyclotron orbits followed by the electron. Simulations suggest that the semiclassical method, which involves here interference between an infinite set of paths, faithfully reproduces the features observed in the quantum solution, even in extreme circumstances, and lends itself to an interpretation of some (though not all) of the rich structure exhibited in this simple problem.Comment: 39 pages, 16 figure

Mechanisms of decoherence in weakly anisotropic molecular magnets

Decoherence mechanisms in crystals of weakly anisotropic magnetic molecules, such as V15, are studied. We show that an important decohering factor is the rapid thermal fluctuation of dipolar interactions between magnetic molecules. A model is proposed to describe the influence of this source of decoherence. Based on the exact solution of this model, we show that at relatively high temperatures, about 0.5 K, the quantum coherence in a V15 molecule is not suppressed, and, in principle, can be detected experimentally. Therefore, these molecules may be suitable prototype systems for study of physical processes taking place in quantum computers.Comment: 4 pages RevTeX, 1 figure (PostScript

Exact propagators on the lattice with applications to diffractive effects

The propagator of the discrete Schr\"odinger equation is computed and its properties are revealed through a Feynman path summation in discrete space. Initial data problems such as diffraction in discrete space and continuous time are studied analytically by the application of the new propagator. In the second part of this paper, the analogy between time propagation and 2D scattering by 1D obstacles is explored. New results are given in the context of diffraction by edges within a periodic medium. A connection with tight-binding arrays and photonic crystals is indicated.Comment: Final version with two appendices. Published in J. Phys. A: Math. Theo

Critical charge instability on verge of the Mott transition and the origin of quantum protection in high-TcT_c cuprates

The concept of topological excitations and the related ground state degeneracy are employed to establish an effective theory of the superconducting state evolving from the Mott insulator for high-Tc cuprates. Casting the Coulomb interaction in terms of composite-fermions via the gauge flux attachment facility, we show that instanton events in the Matsubara "imaginary time," labeled by topological winding numbers, are essential configurations of the phase field dual to the charge. In analogy to the usual phase transition that is characterized by a sudden change of the symmetry, the topological phase transitions are governed by a discontinuous change of the topological numbers signaled by the divergence of the zero-temperature topological susceptibility. This defines a quantum criticality ruled by topologically conserved numbers rather than the Landau principle of the symmetry breaking. We show that in the limit of strong correlations topological charge is linked to the average electronic filling number and the topological susceptibility to the electronic compressibility of the system. We exploit the impact of these nontrivial U(1) instanton phase field configurations for the cuprate phase diagram which displays the "hidden" quantum critical point covered by the superconducting lobe in addition to a sharp crossover between a compressible normal "strange metal" state and a region characterized by a vanishing compressibility, which marks the Mott insulator. Finally, we argue that the existence of robust quantum numbers explains the stability against small perturbation of the system and attributes to the topological "quantum protectorate" as observed in strongly correlated systems.Comment: 23 pages, 12 figure