Boris V. Fine

Typical state of an isolated quantum system with fixed energy and unrestricted participation of eigenstates

This work describes the statistics for the occupation numbers of quantum levels in a large isolated quantum system, where all possible superpositions of eigenstates are allowed provided all these superpositions have the same fixed energy. Such a condition is not equivalent to the conventional microcanonical condition because the latter limits the participating eigenstates to a very narrow energy window. The statistics is obtained analytically for both the entire system and its small subsystem. In a significant departure from the Boltzmann-Gibbs statistics, the average occupation numbers of quantum states exhibit in the present case weak algebraic dependence on energy. In the macroscopic limit, this dependence is routinely accompanied by the condensation into the lowest-energy quantum state. This work contains initial numerical tests of the above statistics for finite systems and also reports the following numerical finding: when the basis states of large but finite random matrix Hamiltonians are expanded in terms of eigenstates, the participation of eigenstates in such an expansion obeys the newly obtained statistics. The above statistics might be observable in small quantum systems, but for the macroscopic systems, it rather re-enforces doubts about self-sufficiency of nonrelativistic quantum mechanics for justifying the Boltzmann-Gibbs equilibrium.

Phase separation in the vicinity of quantum-critical doping concentration : Implications for high-temperature superconductors

A general quantitative measure of the tendency towards phase separation is introduced for systems exhibiting phase transitions or crossovers controlled by charge carrier concentration. This measure is devised for the situations when the quantitative knowledge of various contributions to free energy is incomplete, and is applied to evaluate the chances of electronic phase separation associated with the onset of antiferromagnetic correlations in high-temperature cuprate superconductors. The experimental phenomenology of lanthanum- and yittrium-based cuprates was used as input to this analysis. It is also pointed out that Coulomb repulsion between charge carriers separated by the distances of 1-3 lattice periods strengthens the tendency towards phase separation by accelerating the decay of antiferromagnetic correlations with doping. Overall, the present analysis indicates that cuprates are realistically close to the threshold of phase separation — nanoscale limited or even macroscopic with charge density varying between adjacent crystal planes. PACS numbers:

Equilibrium entanglement vanishes at finite temperature

We show that the equilibrium entanglement of a bipartite system having a finite number of quantum states vanishes at finite temperature, for arbitrary interactions between its constituents and with the environment.

Universal long-time behavior of nuclear spin decays in a solid.

Magnetic resonance studies of nuclear spins in solids are exceptionally well suited to probe the limits of statistical physics. We report experimental results indicating that isolated macroscopic systems of interacting nuclear spins possess the following fundamental property: spin decays that start from different initial configurations quickly evolve towards the same long-time behavior. This long-time behavior is characterized by the shortest ballistic microscopic time scale of the system and therefore falls outside of the validity range for conventional approximations of statistical physics. We find that the nuclear free-induction decay and different solid echoes in hyperpolarized solid xenon all exhibit sinusoidally modulated exponential long-time behavior characterized by identical time constants. This universality was previously predicted on the basis of analogy with resonances in classical chaotic systems.

Hypothesis of two-dimensional stripe arrangement and its implications for the superconductivity in high-Tc cuprates

The hypothesis that holes doped into high-

Regression relation for pure quantum states and its implications for efficient computing.

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Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2.

cuprate superconductors organize themselves in two-dimensional (2D) array of diagonal stripes is discussed, and, on the basis of this hypothesis, a new microscopic model of superconductivity is proposed and solved. The model describes two kinds of hole states localized either inside the stripes or in the antiferromagnetic domains between the stripes. The characteristic energy difference between these two kinds of states is identified with the pseudogap. The onset of superconductivity is caused by the interaction, which is assumed to be mediated by the transverse fluctuations of stripes. The superconducting (SC) order parameter predicted by the model has two components, whose quantum phases exhibit a complex dependence on the the center-of-mass coordinate. The model predictions for the tunneling characteristics and for the dependence of the critical temperature

Largest Lyapunov exponents for lattices of interacting classical spins.

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Long-time behavior of nuclear spin decays in various lattices

on the superfluid density show good quantitative agreement with a number of experiments. The model, in particular, predicts that the SC peaks in the tunneling spectra are asymmetric, only when

Spin-lattice coupling in iron-pnictide superconductors

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