arXiv subjects

Boris V. Fine

Publications and source records attributed to Boris V. Fine.

53 records · Page 3Linked to original sources

arXiv2011

Non-Entangling Channels for Multiple Collisions of Quantum Wave Packets

We consider multiple collisions of quantum wave packets in one dimension. The system under investigation consists of an impenetrable wall and of two hard-core particles with very different masses. The lighter particle bounces between the heavier one and the wall. Both particles are initially represented by narrow Gaussian wave packets. A complete analytical solution of this problem is presented on the basis of a new method. The idea of the method is to decompose the two-particle wave function into a continuous superposition of terms (channels), such that the multiple collisions within each channel do not lead to subsequent entanglement between the two particles. For each channel, the time evolution of the two-particle wave function is completely determined by the motion of the corresponding classical point-like particles; therefore the whole quantum problem is reduced to a classical calculation. The calculation based on the above method reveals the following unexpected result: The entanglement between the two particles first increases with time due to the collisions, but then it begins to decrease, disappearing completely when the light particle becomes too slow to catch up with the heavy one.

quant-ph↗

arXiv2011

Monte-Carlo sampling of energy-constrained quantum superpositions in high-dimensional Hilbert spaces

Recent studies into the properties of quantum statistical ensembles in high-dimensional Hilbert spaces have encountered difficulties associated with the Monte-Carlo sampling of quantum superpositions constrained by the energy expectation value. A straightforward Monte-Carlo routine would enclose the energy constrained manifold within a larger manifold, which is easy to sample, for example, a hypercube. The efficiency of such a sampling routine decreases exponentially with the increase of the dimension of the Hilbert space, because the volume of the enclosing manifold becomes exponentially larger than the volume of the manifold of interest. The present paper explores the ways to optimise the above routine by varying the shapes of the manifolds enclosing the energy-constrained manifold. The resulting improvement in the sampling efficiency is about a factor of five for a 14-dimensional Hilbert space. The advantage of the above algorithm is that it does not compromise on the rigorous statistical nature of the sampling outcome and hence can be used to test other more sophisticated Monte-Carlo routines. The present attempts to optimise the enclosing manifolds also bring insights into the geometrical properties of the energy constrained manifold itself.

quant-ph↗

arXiv2010

Long-time Behavior of Nuclear Spin Decays in Various Lattices

The transverse nuclear magnetic resonance (NMR) decays of $^{129}$Xe in polycrystalline xenon were recently shown to have a universal property: in the long-time regime these decays all converge to the same sinusoidally modulated exponential function irrespective of the initial transverse spin configuration prepared by a sequence of one or more radio frequency pulses. The present work constitutes a more comprehensive survey of this phenomenon. It examines transverse decays for several different isotopic concentrations of $^{129}$Xe, employs additional pulse sequences, and performs similar measurements in a different material: $^{19}$F in single-crystal and polycrystalline CaF$_2$. We additionally verified the polycrystalline nature of our frozen xenon samples by X-ray diffraction measurements. With the possible exception of polycrystalline CaF$_2$ where the observation of the long-time behavior is limited by the experimental resolution, all these systems display the long-time universal behavior characterized by particular values of the exponential decay coefficient and beat frequency that were unique for each lattice. This behavior has been theoretically predicted based on the notion of microscopic chaos.

nucl-ex↗

arXiv2010

An alternative to the conventional micro-canonical ensemble

Usual approach to the foundations of quantum statistical physics is based on conventional micro-canonical ensemble as a starting point for deriving Boltzmann-Gibbs (BG) equilibrium. It leaves, however, a number of conceptual and practical questions unanswered. Here we discuss these questions, thereby motivating the study of a natural alternative known as Quantum Micro-Canonical (QMC) ensemble. We present a detailed numerical study of the properties of the QMC ensemble for finite quantum systems revealing a good agreement with the existing analytical results for large quantum systems. We also propose the way to introduce analytical corrections accounting for finite-size effects. With the above corrections, the agreement between the analytical and the numerical results becomes very accurate. The QMC ensemble leads to an unconventional kind of equilibrium, which may be realizable after strong perturbations in small isolated quantum systems having large number of levels. We demonstrate that the variance of energy fluctuations can be used to discriminate the QMC equilibrium from the BG equilibrium. We further suggest that the reason, why BG equilibrium commonly occurs in nature rather than the QMC-type equilibrium, has something to do with the notion of quantum collapse.

cond-mat.stat-mech↗

arXiv2010

Implications of spin vortex scenario for 1/8-doped lanthanum cuprates

Superlattice of spin vortices has been proposed in an earlier article as an alternative to the stripe interpretation of spin modulations in 1/8-doped lanthanum cuprates. The present article addresses several additional characteristics of the spin vortex lattice, namely: (i) the nature of extended charge states; (ii) the position of neutron spin peaks as a function of doping; and (iii) the absence of higher order spin harmonics. All these characteristics afford straightforward connection to the experimental results produced by angle-resolved photoemission spectroscopy, resistivity measurements, and neutron scattering.

cond-mat.supr-con↗

arXiv2009

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 micro-canonical 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 reenforces doubts about self-sufficiency of non-relativistic quantum mechanics for justifying the Boltzmann-Gibbs equilibrium.

cond-mat.stat-mech↗

arXiv2008

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 timescale 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.

cond-mat.stat-mech↗

arXiv2007

Interpretation of low-temperature nuclear quadrupole resonance spectra in La(1.875)Ba(0.125)CuO(4) in terms of two-dimensional spin superstructure

This paper reanalyzes the low temperature nuclear quadrupole resonance (NQR) experiments in La(1.875)Ba(0.125)CuO(4) by Hunt et al. [Phys. Rev. B 64, 134565 (2001)] in an attempt to determine the dimensionality of spin modulations in this and other compounds of the lanthanum family of high temperature cuprate superconductors. It is concluded that the shape of the NQR spectra obtained by Hunt et al. favors the two-dimensional pattern of spin modulations known as "grid" or "checkerboard". The paper also contains the discussion of charge patterns, which can accompany the above spin modulation.

cond-mat.str-el↗

arXiv2007

Magnetic vortices instead of stripes: another interpretation of magnetic neutron scattering in lanthanum cuprates

It is proposed, that a two-dimensional magnetic superstructure closely related to the one mentioned recently by Christensen et al. [cond-mat/0608204] constitutes a viable interpretation of the four-fold splitting of the magnetic (π, π) peak in lanthanum cuprates. (This splitting is usually interpreted as the evidence for stripes.) The superstructure in question has the topology of the square crystal of magnetic vortices with approximate periodicity (4a x 4a). This vortex crystal exhibits no magnetic antiphase lines. It is shown that such a superstructure is magnetically stable in the approximation of staggered spin polarizations, and that it should be accompanied by charge modulation characterized by charge peaks at the positions observed experimentally.

cond-mat.str-el↗

arXiv2007

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.

cond-mat.str-el↗

arXiv2005

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

The hypothesis that holes doped into high-Tc 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 superconducting (SC) order parameter predicted by the model has two components, whose 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 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 the ratio of the SC gap to the critical temperature is greater than 4. It is also proposed that, at least in some high-Tc cuprates, there exist two different superconducting states corresponding to the same doping concentration and the same critical temperature. Finally, the checkerboard pattern in the local density of states observed by scanning tunneling microscopy in Bi-2212 is interpreted as coming from the states localized around the centers of stripe elements forming the 2D superstructure.

cond-mat.supr-con↗

arXiv2005

Temperature dependence of the superconducting gap in high-Tc cuprates

It is proposed that (i) the temperature dependence of the superconducting gap Delta(T) in high-Tc cuprates can be predicted just from the knowledge of Delta(0) and the critical temperature Tc; and, in particular, (ii) Delta(0)/Tc > 4 implies that Delta(Tc) is not equal to zero, while Delta(0)/Tc < 4 corresponds to Delta(Tc) = 0. A number of tunneling experiments appear to support the above proposition, and, furthermore, show reasonable quantitative agreement with a model (cond-mat/0308428), which is based on the two-dimensional stripe hypothesis.

cond-mat.supr-con↗

arXiv2004

On the long-time behavior of spin echo and its relation to free induction decay

It is predicted that (i) spin echoes have two kinds of generic long-time decays: either simple exponential, or a superposition of a monotonic and an oscillatory exponential decays; and (ii) the long-time behavior of spin echo and the long-time behavior of the corresponding homogeneous free induction decay are characterized by the same time constants. This prediction extends to various echo problems both within and beyond nuclear magnetic resonance. Experimental confirmation of this prediction would also support the notion of the eigenvalues of time evolution operators in large quantum systems.

cond-mat.other↗

arXiv2004

Universal Long-Time Relaxation on the Lattices of Classical Spins: Markovian Behavior on non-Markovian Timescales

The long-time behavior of certain fast-decaying infinite temperature correlation functions on one-, two- and three-dimensional lattices of classical spins with various kinds of nearest-neighbor interactions is studied numerically, and evidence is presented that the functional form of this behavior is either simple exponential or exponential multiplied by cosine. Due to the fast characteristic timescale of the long-time decay, such a universality cannot be explained on the basis of conventional Markovian assumptions. It is suggested that this behavior is related to the chaotic properties of the spin dynamics.

cond-mat.stat-mech↗

arXiv2004

Long-Time Relaxation on Spin Lattice as Manifestation of Chaotic Dynamics

The long-time behavior of the infinite temperature spin correlation functions describing the free induction decay in nuclear magnetic resonance and intermediate structure factors in inelastic neutron scattering is considered. These correlation functions are defined for one-, two- and three-dimensional infinite lattices of interacting spins both classical and quantum. It is shown that, even though the characteristic timescale of the long-time decay of the correlation functions considered is non-Markovian, the generic functional form of this decay is either simple exponential or exponential multiplied by cosine. This work contains (i) summary of the existing experimental and numerical evidence of the above asymptotic behavior; (ii) theoretical explanation of this behavior; and (iii) semi-empirical analysis of various factors discriminating between the monotonic and the oscillatory long-time decays. The theory is based on a fairly strong conjecture that, as a result of chaos generated by the spin dynamics, a Brownian-like Markovian description can be applied to the long-time properties of ensemble average quantities on a non-Markovian timescale. The formalism resulting from that conjecture can be described as ``correlated diffusion in finite volumes.''

cond-mat.stat-mech↗

arXiv2004

Superconductivity in the background of two-dimensional stripe superstructure

I propose a superconductivity model, which is based on the assumption that stripes in high-Tc cuprates (a) exist and (b) organize themselves in a two-dimensional superstructure. The model describes hole states, which are localized either inside the stripes or in the antiferromagnetic domains between the stripes. The superconductivity in this model emerges due to the interaction, which is, presumably, mediated by the transverse fluctuations of stripes. The tunnelling density of states obtained from the mean field solution of the model is asymmetric with respect to the chemical potential, has Van Hove singularity identified as a superconducting peak, and, in one of the model regimes, has linear functional form in the vicinity of the chemical potential. The relation between the critical temperature and the zero-temperature superfluid density has ``fish-like'' form, which quantitatively resembles experimental data. The superconducting order parameter obtained from this model has two components exhibiting non-trivial phase and sign change under translations in real space.

cond-mat.supr-con↗

arXiv1997

NMR Spin-Spin Relaxation as Kinetics in Spin Phase Space

A new approach is presented that treats NMR spin-spin relaxation as kinetics in spin phase space. The approach is applied to free induction decay (FID) in solids containing equivalent nuclear spins 1/2. The description obtained does not involve adjustable parameters. As an example, the calculation is performed for the fluorine FID in calcium fluoride, and the results are in good agreement with experiment.

cond-mat↗