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We propose a technique for polarizing and cooling finite many-body classical systems using feedback control. The technique requires the system to have one collective degree of freedom conserved by the internal dynamics. The fluctuations of other degrees of freedom are then converted into the growth of the conserved one. The proposal is validated using numerical simulations of classical spin systems in a setting representative of Nuclear Magnetic Resonance experiments. In particular, we were able to achieve 90 percent polarization for a lattice of 1000 classical spins starting from an unpolarized infinite temperature state., Comment: 5 pages, 3 figures

Hysteresis underlies a large number of phase transitions in solids, giving rise to exotic metastable states that are otherwise inaccessible. Here, we report an unconventional hysteretic transition in a quasi-2D material, EuTe_{4}. By combining transport, photoemission, diffraction, and x-ray absorption measurements, we observe that the hysteresis loop has a temperature width of more than 400 K, setting a record among crystalline solids. The transition has an origin distinct from known mechanisms, lying entirely within the incommensurate charge density wave (CDW) phase of EuTe_{4} with no change in the CDW modulation periodicity. We interpret the hysteresis as an unusual switching of the relative CDW phases in different layers, a phenomenon unique to quasi-2D compounds that is not present in either purely 2D or strongly coupled 3D systems. Our findings challenge the established theories on metastable states in density wave systems, pushing the boundary of understanding hysteretic transitions in a broken-symmetry state.

We present the state-of-the-art performance of air-coupled thermophones made of thin, freestanding films of randomly oriented single-walled carbon nanotubes (SWCNTs). The work demonstrates both experimentally and theoretically that extremely low heat capacity per unit area of SWCNT films allows centimeter-sized thermophones to achieve record sound pressures (normalized to the input power and geometry) in the frequency range of 1–100 kHz. Our SWCNT films have an aerogel structure. We systematically investigated their thermoacoustic performance as a function of the film thickness and purity. On the theoretical side, we obtained an analytic formula for the sound pressure in the ultrasound region and confirmed it by experiments and numerical simulations.

We formulate a dynamical model to describe a photo-induced charge density wave (CDW) quench transition and apply it to recent multi-probe experiments on LaTe$_3$ [A. Zong et al., Nat. Phys. 15, 27 (2019)]. Our approach relies on coupled time-dependent Ginzburg-Landau equations tracking two order parameters that represent the modulations of the electronic density and the ionic positions. We aim at describing the amplitude of the order parameters under the assumption that they are homogeneous in space. This description is supplemented by a three-temperature model, which treats separately the electronic temperature, temperature of the lattice phonons with stronger couplings to the electronic subsystem, and temperature of all other phonons. The broad scope of available data for LaTe$_3$ and similar materials as well as the synergy between different time-resolved spectroscopies allow us to extract model parameters. The resulting calculations are in good agreement with ultra-fast electron diffraction experiments, reproducing qualitative and quantitative features of the CDW amplitude evolution during the initial few picoseconds after photoexcitation., Comment: 21 pages, 14 figures; this version is almost identical to the published version; comparing to the earlier arXiv submission, current version contains a new figure (Fig.10), and a broader discussion of theoretical results and approximations

Nuclear spin-1/2 lattices where each spin has a small effective number of interacting neighbors represent a particular challenge for first-principles calculations of free induction decays (FIDs) observed by nuclear magnetic resonance (NMR). The challenge originates from the fact that these lattices are far from the limit where classical spin simulations perform well. Here we use the recently developed method of hybrid quantum-classical simulations to compute nuclear FIDs for $^{29}$Si-enriched silicon and fluorapatite. In these solids, small effective number of interacting neighbors is either due to the partition of the lattice into pairs of strongly coupled spins (silicon), or due to the partition into strongly coupled chains (fluorapatite). We find a very good overall agreement between the hybrid simulation results and the experiments. In addition, we introduce an extension of the hybrid method, which we call the method of "coupled quantum clusters". It is tested on $^{29}$Si-enriched silicon and found to exhibit excellent performance., Comment: 19 pages, 14 figures

Revivals of initial non-equilibrium states is an ever-present concern for the theory of dynamic thermalization in many-body quantum systems. Here we consider a nonintegrable lattice of interacting spins 1/2 and show how to construct a quantum state such that a given spin 1/2 is maximally polarized initially and then exhibits an almost complete recovery of the initial polarization at a predetermined moment of time. An experimental observation of such revivals may be utilized to benchmark quantum simulators with a measurement of only one local observable. We further propose to utilize these revivals for a delayed disclosure of a secret., Comment: 5 pages, 3 figures

Upon excitation with an intense laser pulse, a symmetry-broken ground state can undergo a non-equilibrium phase transition through pathways different from those in thermal equilibrium. The mechanism underlying these photoinduced phase transitions has long been researched in the study of condensed matter systems1, but many details in this ultrafast, non-adiabatic regime still remain to be clarified. To this end, we investigate the light-induced melting of a unidirectional charge density wave (CDW) in LaTe3. Using a suite of time-resolved probes, we independently track the amplitude and phase dynamics of the CDW. We find that a fast (approximately 1 picosecond) recovery of the CDW amplitude is followed by a slower re-establishment of phase coherence. This longer timescale is dictated by the presence of topological defects: long-range order is inhibited and is only restored when the defects annihilate. Our results provide a framework for understanding other photoinduced phase transitions by identifying the generation of defects as a governing mechanism. Three different ultrafast probes investigate a non-adiabatic phase transition and find substantial evidence of topological defects inhibiting the reformation of the equilibrium phase.

We introduce a microscopic model aimed at describing the behavior of fermionic excitations in the background of a magnetic texture called a ``spin-vortex checkerboard.'' This texture was proposed previously as a possible alternative to stripes to interpret the experimental phenomenology of spin and charge modulations in 1/8-doped lanthanum cuprates. The model involves two kinds of interacting fermionic excitations residing in spin-rich and spin-poor regions of the modulated structure. It is a generalization of another model developed earlier for the so-called ``grid checkerboard.'' The principal terms of our model describe the decay of fermionic pairs belonging to spin-poor regions into single fermions occupying spin-rich regions and vice versa. These terms induce intricate fermionic correlations throughout the system but fall short of inducing superconductivity unless arbitrarily small hopping terms are added to the model Hamiltonian. We present the mean-field solution of the model, including, in particular, the temperature dependence of the energy gap. The latter is found to be in good overall agreement with available experimental data for high-${T}_{c}$ cuprate superconductors.

We define the notion of mutual quantum measurements of two macroscopic objects and investigate the effect of these measurements on the velocities of the objects. We show that multiple mutual quantum measurements can lead to an effective force emerging as a consequence of asymmetric diffusion in the velocity space. We further show that, under a certain set of assumptions involving the measurements of mutual Doppler shifts, the above force can reproduce Newton's law of gravitation. Such a mechanism would explain the equivalence between the gravitational and the inertial masses. For a broader class of measurements, the emergent force can also lead to corrections to Newton's gravitation., 12 pages, 3 figures

The combination of EUV based time-resolved Angle-Resolved-Photo-Electron-Spectroscopy (trARPES), Ultrafast-Electron-Diffraction (UED) and Transient-Optical-Spectroscopy (TOS) facilitates a comprehensive study and all-embracing analysis of correlated dynamics, exemplified on the system of Charge-Density-Waves (CDW’s) in rare earth tritellurides (RTe3).

We propose a method of estimating ergodization time of a chaotic many-particle system by monitoring equilibrium noise before and after time reversal of dynamics (Loschmidt echo). The ergodization time is defined as the characteristic time required to extract the largest Lyapunov exponent from a system's dynamics. We validate the method by numerical simulation of an array of coupled Bose-Einstein condensates in the regime describable by the discrete Gross-Pitaevskii equation. The quantity of interest for the method is a counterpart of out-of-time-order correlators (OTOCs) in the quantum regime., v4. The relation to quantum systems and out-of-time-order correlators (OTOCs) are added. A quantum counterpart of the maximum classical Lyapunov exponent is defined. The supplementary material added

The lanthanum family of high-temperature cuprate superconductors is known to exhibit both spin and charge electronic modulations around a doping level of 1/8. We assume that these modulations have the character of a two-dimensional spin-vortex checkerboard and investigate whether this assumption is consistent with the Fermi surface and the pseudogap measured by angle-resolved photoemission spectroscopy. We also explore the possibility of observing quantum oscillations of transport coefficients in such a background. These investigations are based on a model of noninteracting spin-1/2 fermions hopping on a square lattice and coupled through spins to a magnetic field imitating a spin-vortex checkerboard. The main results of this paper include (i) a calculation of the Fermi surface containing Fermi arcs at the positions in the Brillouin zone largely consistent with experiments, (ii) identification of factors complicating the observations of quantum oscillations in the presence of spin modulations, and (iii) an investigation of the symmetries of the resulting electronic energy bands, which, in particular, indicates that each band is doubly degenerate and has at least one conical point, where it touches another doubly degenerate band. We discuss possible implications these cones may have for the transport properties and the pseudogap.

We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble "stable" if a small number of local measurements cannot significantly modify the total-energy distribution representing the ensemble. First, we numerically calculate the evolution of the stability measure introduced in our previous work [Phys. Rev. E 94, 062106 (2016)] for an ensemble representing a mixture of two canonical ensembles with very different temperatures in a periodic chain of interacting spins-1/2. Second, we propose other possible stability measures and discuss their advantages and disadvantages. We also show that, for small system sizes available to numerical simulations of local measurements, finite-size effects are rather pronounced., 5 pages, 3 figures

We propose a method for protecting fragile quantum superpositions in many-particle systems from dephasing by external classical noise. We call superpositions "fragile" if dephasing occurs particularly fast, because the noise couples very differently to the superposed states. The method consists of letting a quantum superposition evolve under the internal thermalization dynamics of the system, followed by a time reversal manipulation known as Loschmidt echo. The thermalization dynamics makes the superposed states almost indistinguishable during most of the above procedure. We validate the method by applying it to a cluster of spins-1/2., Comment: 5 pages, 3 figures

We propose theoretically an experimentally realizable method to demonstrate the Lyapunov instability and to extract the value of the largest Lyapunov exponent for a chaotic many-particle interacting system. The proposal focuses specifically on a lattice of coupled Bose-Einstein condensates in the classical regime describable by the discrete Gross-Pitaevskii equation. We suggest to use imperfect time reversal of the system's dynamics known as the Loschmidt echo, which can be realized experimentally by reversing the sign of the Hamiltonian of the system. The routine involves tracking and then subtracting the noise of virtually any observable quantity before and after the time reversal. We support the theoretical analysis by direct numerical simulations demonstrating that the largest Lyapunov exponent can indeed be extracted from the Loschmidt echo routine. We also discuss possible values of experimental parameters required for implementing this proposal.

We investigate numerically and analytically the heating process in ergodic clusters of interacting spins 1/2 subjected to periodic pulses of external magnetic field. Our findings indicate that there is a threshold for the pulse strength below which the heating is suppressed. This threshold decreases with the increase of the cluster size, approaching zero in the thermodynamic limit; yet it should be observable in clusters with fairly large Hilbert spaces. We obtain the above threshold quantitatively as a condition for the breakdown of the golden rule in the second-order perturbation theory. It is caused by the phenomenon of dynamic localization., Comment: Final version; Main article: 5 pages, 4 figures; Supplement: 3 pages, 2 figures

We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the total energy of the system. We apply this criterion to lattices of spins-1/2, thereby showing that the canonical ensemble is nearly stable, whereas statistical ensembles with much broader energy distributions are not stable. In the context of the foundations of quantum statistical physics, this result justifies the use of statistical ensembles with narrow energy distributions such as canonical or microcanonical ensembles., 14 pages, 5 figures

Comin et al. [Science 347, 1335 (2015)] have interpreted their resonant X-ray scattering experiment as indicating that charge inhomogeneities in the family of high-temperature superconductors YBa2Cu3O6+y (YBCO) have the character of one-dimensional stripes rather than two-dimensional checkerboards. The present comment shows that one cannot distinguish between stripes and checkerboards on the basis of the above experiment., Comment: Text close to the published version, 3 pages, 1 figure. Authors response to this comment: Science v.351, p.235-b (2016)

A cluster of spins $1/2$ of a finite size can be regarded as a basic building block of a spin texture in high-temperature cuprate superconductors. If this texture has the character of a network of weakly coupled spin clusters, then spin excitation spectra of finite clusters are expected to capture the principal features of the experimental spin response. We calculate spin excitation spectra of several clusters of spins $1/2$ coupled by Heisenberg interaction. We find that the calculated spectra exhibit a high degree of variability representative of the actual phenomenology of curates, while, at the same time, reproducing a number of important features of the experimentally measured spin response. Among such features are the spin gap, the broad peak around $\hbar \omega\simeq (40 - 70)$ meV and the sharp peak at zero frequency. The latter feature emerges due to transitions inside the ground-state multiplet of the so-called "uncompensated" clusters with an odd number of spins.

We consider strong spin-lattice and spin-phonon coupling in iron pnictides and discuss its implications on superconductivity. Strong magneto-volume effect in iron compounds has long been known as the Invar effect. Fe pnictides also exhibit this effect, reflected in particular on the dependence of the magnetic moment on the atomic volume of Fe defined by the positions of the nearest neighbor atoms. Through the phenomenological Landau theory, developed on the basis of the calculations by the density functional theory (DFT) and the experimental results, we quantify the strength of the spin-lattice interaction as it relates to the Stoner criterion for the onset of magnetism. We suggest that the coupling between electrons and phonons through the spin channel may be sufficiently strong to be an important part of the superconductivity mechanism in Fe pnictides.

We investigate the limits of effectiveness of classical spin simulations for predicting free induction decays (FIDs) measured by solid-state nuclear magnetic resonance (NMR) on systems of quantum nuclear spins. The specific limits considered are associated with the range of interaction, the size of individual quantum spins and the long-time behavior of the FID signals. We compare FIDs measured or computed for lattices of quantum spins (mainly spins 1/2) with the FIDs computed for the corresponding lattices of classical spins. Several cases of excellent quantitative agreement between quantum and classical FIDs are reported along with the cases of gradually decreasing quality of the agreement. We formulate semi-empirical criteria defining the situations, when classical simulations are expected to accurately reproduce quantum FIDs. Our findings indicate that classical simulations may be a quantitatively accurate tool of first principles calculations for a broad class of macroscopic systems, where individual quantum microscopic degrees of freedom are far from the classical limit., Comment: 6 pages, 3 figures

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.

We numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered lattices. In the former case, the quench consists of sudden switching-on the off-diagonal elements of the Hamiltonian. In the latter case, it is sudden switching-on of the hopping between adjacent lattice sites. The quench-induced ensembles are compared with the so-called "quantum micro-canonical" (QMC) ensemble describing quantum superpositions with fixed energy expectation values. Our main finding is that quantum quenches with sparse random matrices having one special diagonal element lead to the condensation phenomenon predicted for the QMC ensemble. Away from the QMC condensation regime, the overall agreement with the QMC predictions is only qualitative for both random matrices and disordered lattices but with some cases of a very good quantitative agreement. In the case of disordered lattices, the QMC ensemble can be used to estimate the probability of finding a particle in a localized or delocalized eigenstate., 10 pages, 9 figures

We show that macroscopic nonintegrable lattices of spins 1/2, which are often considered to be chaotic, do not exhibit the basic property of classical chaotic systems, namely, exponential sensitivity to small perturbations. We compare chaotic lattices of classical spins and nonintegrable lattices of spins 1/2 in terms of their magnetization responses to imperfect reversal of spin dynamics known as Loschmidt echo. In the classical case, magnetization exhibits exponential sensitivity to small perturbations of Loschmidt echoes, which is characterized by twice the value of the largest Lyapunov exponent of the system. In the case of spins 1/2, magnetization is only power-law sensitive to small perturbations. Our findings imply that it is impossible to define Lyapunov exponents for lattices of spins 1/2 even in the macroscopic limit. At the same time, the above absence of exponential sensitivity to small perturbations is an encouraging news for the efforts to create quantum simulators. The power-law sensitivity of spin 1/2 lattices to small perturbations is predicted to be measurable in nuclear magnetic resonance experiments., 12 pages, 8 figures, minor changes, new references

We perform a numerical investigation of the Lyapunov spectra of chaotic dynamics in lattices of classical spins in the vicinity of second-order ferromagnetic and antiferromagnetic phase transitions. On the basis of this investigation, we identify a characteristic of the shape of the Lyapunov spectra, the "G-index", which exhibits a sharp peak as a function of temperature at the phase transition, provided the order parameter is capable of sufficiently strong dynamic fluctuations. As a part of this work, we also propose a general numerical algorithm for determining the temperature in many-particle systems, where kinetic energy is not defined., Comment: 9 pages, 11 figures

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., Comment: 4 pages, 1 Postscript figure, submitted to PRL

Free induction decay (FID) measured by nuclear magnetic resonance (NMR) in a polycrystalline solid is the isotropic average of the FIDs for individual single crystallites. It has been recently proposed theoretically and verified experimentally that the long-time behavior of single-crystal FIDs has the universal form of exponentially decaying sinusoidal oscillations. Polycrystalline averaging complicates the situation theoretically, while the available experimental evidence is also ambiguous. Exponentially decaying sinusoidal oscillations have been observed for Xe-129 in polycrystalline solid xenon but not for F-19 in the powder of CaF2. In this paper, we present the first principles FID calculations for the powders of both CaF2 and solid xenon. In both cases, the asymptotic long-time behavior has the expected form of exponentially decaying sinusoidal oscillations, which is determined by the single crystallite FID with the slowest exponential decay. However, this behavior appears only at rather small values of the signal that have not yet been measured in experiments. At intermediate times accessible experimentally, a polycrystalline FID depends on the distribution of the exponential decay constants and oscillation frequencies for single crystallite FIDs. In CaF2, these parameters are relatively broadly distributed, and as a result, the sinusoidal long-time oscillations become somewhat washed out. In contrast, the single crystallite parameters are more clustered in solid xenon, and, as a result, the experimentally observable range is characterized by well-defined oscillation frequency and exponential decay constant even though both of these parameters do not represent the true long-time behavior. The above difference of the intermediate FID behavior originates from the difference of the crystal structures of solid xenon and CaF2., Comment: 16 pages, 5 figures

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., 9 pages, 3 figures

We investigate the dimensionality of inhomogeneous spin modulation patterns in the cuprate family of high-temperature superconductors with particular focus on 1/8-doped lanthanum cuprates. We compare one-dimensional stripe modulation pattern with two-dimensional checkerboard of spin vortices in the context of nuclear quadrupole resonance(NQR) and muon spin rotation(muSR) experiments. In addition, we also consider the third pattern, a two-dimensional superposition of spin spirals. Overall, we have found that none of the above patterns leads to a consistent interpretation of the two types of experiments considered. This, in particular, implies that the spin vortex checkerboard cannot be ruled out on the basis of available NQR/muSR experimental results., Comment: 6 pages, 2 figures

We investigate how generic the onset of chaos in interacting many-body classical systems is in the context of lattices of classical spins with nearest-neighbor anisotropic couplings. Seven large lattices in different spatial dimensions were considered. For each lattice, more than 2000 largest Lyapunov exponents for randomly sampled Hamiltonians were numerically computed. Our results strongly suggest the absence of integrable nearest-neighbor Hamiltonians for the infinite lattices except for the trivial Ising case. In the vicinity of the Ising case, the largest Lyapunov exponents exhibit a power-law growth, while further away they become rather weakly sensitive to the Hamiltonian anisotropy. We also provide an analytical derivation of these results.

We show numerically that a finite isolated cluster of interacting spins 1/2 exhibits a surprising non-thermal statistics when subjected to a series of small non-adiabatic perturbations by external magnetic field. The resulting occupations of energy eigenstates are significantly higher than the thermal ones on both the low and the high ends of the energy spectra. This behavior semi-quantitatively agrees with the statistics predicted for the so-called "quantum micro-canonical" (QMC) ensemble, which includes all possible quantum superpositions with a given energy expectation value. Our findings also indicate that the eigenstates of the perturbation operators are generically localized in the energy basis of the unperturbed Hamiltonian. This kind of localization possibly protects the thermal behavior in the macroscopic limit., version as accepted to PRL. Main article: 4 pages, 4 figures. Supplement: 5 pages, 10 figures

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., 9 pages, 7 figures, accepted for publication in European Physical Journal D

Recent theoretical work on the role of microscopic chaos in the dynamics and relaxation of many-body quantum systems has made several experimentally confirmed predictions about the systems of interacting nuclear spins in solids, focusing, in particular, on the shapes of spin echo responses measured by nuclear magnetic resonance (NMR). These predictions were based on the idea that the transverse nuclear spin decays evolve in a manner governed at long times by the slowest decaying eigenmode of the quantum system, analogous to a chaotic resonance in a classical system. The present paper extends the above investigations both theoretically and experimentally. On the theoretical side, the notion of chaotic eigenmodes is used to make predictions about the relationships between the long-time oscillation phase of the nuclear free induction decay (FID) and the amplitudes and phases of spin echoes. On the experimental side, the above predictions are tested for the nuclear spin decays of F-19 in CaF2 crystals and Xe-129 in frozen xenon. Good agreement between the theory and the experiment is found., Comment: 20 pages, 9 figures, significant new experimental content in comparison with version 1

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.

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., 25 pages, 6 figures

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., 20 pages, 3 figures

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., 4 pages, 2 figures

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., Comment: 4 pages main paper + 3 pages supporting material, 3 figures

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

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 (\pi, \pi) 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., Comment: 4 pages, 2 figures, final version

This paper reanalyzes the low temperature nuclear quadrupole resonance (NQR) experiments in ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}\mathrm{Cu}{\mathrm{O}}_{4}$ 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.

We investigate the sensitivity of nonintegrable large-spin quantum lattices to small perturbations with a particular focus on the time reversal experiments known in statistical physics as "Loschmidt echoes" and in nuclear magnetic resonance (NMR) as "magic echoes". Our numerical simulations of quantum spin-$7\frac{1}{2}$ clusters indicate that there is a regime, where Loschmidt echoes exhibit nearly exponential sensitivity to small perturbations with characteristic constant approximately equal to twice the value of the largest Lyapunov exponent of the corresponding classical spin clusters. The above theoretical results are verifiable by NMR experiments on solids containing large-spin nuclei., Comment: 4 pages, 1 figure

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.

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., 2 pages, no figures, first submitted on July 22, 2004

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.