Eigenmodes in the long-time behavior of a coupled spin system measured with nuclear magnetic resonance

The many-body quantum dynamics of dipolar coupled nuclear spins I=1/2 on an otherwise isolated cubic lattice are studied with nuclear magnetic resonance. By increasing the signal-to-noise ratio by 2 orders of magnitude compared with previous reports for the free induction decay (FID) of (19)F in CaF(2) we obtain new insight into its long-time behavior. We confirm that the tail of the FID is an exponentially decaying cosine, but our measurements reveal a second decay mode with comparable frequency but twice the decay constant. This result is in agreement with a recent theoretical prediction for the FID in terms of eigenvalues for the time evolution of chaotic many-body quantum systems.     

Long-Time Tails, Weak Localization, and Classical and Quantum Critical Behavior

An overview is given of the long-time and long-distance behavior of correlation functions in both classical and quantum statistical mechanics. After a simple derivation of the classical long-time tails in equilibrium time correlation functions, we discuss analogous long-distance phenomena in nonequilibrium classical systems. The paper then draws analogies between these phenomena and similar effects in quantum statistical mechanics, with emphasis on the soft modes that underly long-time tails and related phenomena. We also elucidate the interplay between critical phenomena and long-time tails, using the classical liquid-gas critical point and the quantum ferromagnetic transition as examples.     

Information-Theoretic Features of Many Fermion Systems: An Exploration Based on Exactly Solvable Models

Finite quantum many fermion systems are essential for our current understanding of Nature. They are at the core of molecular, atomic, and nuclear physics. In recent years, the application of information and complexity measures to the study of diverse types of many-fermion systems has opened a line of research that elucidates new aspects of the structure and behavior of this class of physical systems. In this work we explore the main features of information and information-based complexity indicators in exactly soluble many-fermion models of the Lipkin kind. Models of this kind have been extremely useful in shedding light on the intricacies of quantum many body physics. Models of the Lipkin kind play, for finite systems, a role similar to the one played by the celebrated Hubbard model of solid state physics. We consider two many fermion systems and show how their differences can be best appreciated by recourse to information theoretic tools. We appeal to information measures as tools to compare the structural details of different fermion systems. We will discover that few fermion systems are endowed by a much larger complexity-degree than many fermion ones. The same happens with the coupling-constants strengths. Complexity augments as they decrease, without reaching zero. Also, the behavior of the two lowest lying energy states are crucial in evaluating the system’s complexity.     

Dynamic criteria for melting in two dimensions

The two-dimensional (2D) melting transition is analyzed on the basis of the long-time behavior of a modified Lindemann parameter in 2D gamma(L)(t) and the bond-angular correlation function g(6)(t). Using video microscopy complete positional data are obtained over five decades in time for an ensemble of superparamagnetic colloidal particles confined to an air-water interface. We find that each of the three phases (solid/hexatic/isotropic liquid) is uniquely characterized by the long-time behavior of gamma(L)(t), g(6)(t), and the non-Gaussian parameter of the relative neighbor-neighbor displacement.     

Algorithmic treatment of the spin-echo effect

We analyze the apparent increase in entropy in the course of the spin-echo effect using algorithmic information theory. We show that although the state of the spins quickly becomes algorithmically complex, then simple again during the echo, the overall complexity of spins together with the magnetic field grows slowly, as the logarithm of the elapsed time. This slow increase in complexity is reflected in an increased difficulty in taking advantage of the echo pulse. Our discussion illustrates the fundamental role of algorithmic information content in the formulation of statistical physics, including the second law of thermodynamics, from the viewpoint of the observer.     

Long time evolution of a spin interacting with a spin bath in arbitrary magnetic field

We introduce a completely different method to calculate the evolution of a spin interacting with a sufficient large spin bath,especially suitable for treating the central spin model in a quantum dot(QD).With only an approximation on the envelope of central spin,the symmetry can be exploited to reduce a huge Hilbert space which cannot be calculated with computers to many small ones which can be solved exactly.This method can be used to calculate spin-bath evolution for a spin bath containing many(say,1000)spins,without a perturbative limit such as strong magnetic field condition,and works for long-time regime with sufficient accuracy.As the spin-bath evolution can be calculated for a wide range of time and magnetic field,an optimal dynamic of spin flip-flop can be found,and more sophisticated approaches to achieve extremely high polarization of nuclear spins in a QD could be developed.     

Analytical and Numerical Studies of the One-Dimensional Spin Facilitated Kinetic Ising Model

The one-dimensional spin facilitated kinetic Ising model is studied analytically using the master equation and by simulations. The local state of the spins (corresponding to mobile and immobile cells) can change depending on the state of the neighbored spins, which reflects the high cooperativity inherent in glassy materials. The short-time behavior is analyzed using a Fock space representation for the master equation. The hierarchy of evolution equations for the averaged spin state and the time dependence of the spin autocorrelation function are calculated with different methods (mean-field theory, expansion in powers of the time, partial summation) and compared with numerical simulations. The long-time behavior can be obtained by mapping the one-dimensional spin facilitated kinetic Ising model onto a one-dimensional diffusion model containing birth and death processes. The resulting master equation is solved by van Kampen's size expansion, which leads to a Langevin equation with Gaussian noise. The predicted autocorrelation function and the global memory offer in the long-time limit a screened algebraic decay and a stretched exponential decay, respectively, consistent with numerical simulations.     

Majorana modes in solid state systems and its dynamics

We review the properties of Majorana fermions in particle physics and point out that Majorana modes in solid state systems are significantly different. The key reason is the concept of anti-particle in solid state systems is different from its counterpart in particle physics. We define Majorana modes as the eigenstates of Majorana operators and find that they can exist both at edges and in the bulk. According to our definition, only one single Majorana mode can exist in a system no matter at edges or in the bulk. Kitaev’s spinless p-wave superconductor is used to illustrate our results and the dynamical behavior of the Majorana modes.     

Random matrix theory models of electric grid topology

The random matrix theory is useful in the study of large systems such as electric grids. These transmission systems can be modeled as complex networks, with high-voltage lines the edges that connect nodes representing power plants and substations. We draw upon established literature of complex systems theory and introduce methods from nuclear and statistical physics to identify new characteristics of these networks. We show that most grids can be characterized by the Gaussian Orthogonal Ensemble, an indicator of chaos in many complex systems. Under certain circumstances, however, grids may be described by Poisson statistics, an indicator of regularity. We use the random matrix formalism to describe the interconnection of multiple grids and construct a simple model of a distributed grid.     

Dynamic nuclear polarisation in metallic silver

Dynamic nuclear polarisation is a well established technique, which has been used to produce polarised targets for experiments in nuclear physics. This paper suggests that the nuclei spins in metallic silver may be polarised by inclusion of erbium as a small impurity with an electronic spin.     

Isotopically controlled semiconductors

A review of recent research involving isotopically controlled semiconductors is presented. Studies with isotopically enriched semiconductor structures experienced a dramatic expansion at the end of the cold war when significant quantities of enriched isotopes of elements forming semiconductors became available for worldwide collaborations. Isotopes of an element differ in nuclear mass, may have different nuclear spins and undergo different nuclear reactions. Among the latter, the capture of thermal neutrons, which can lead to neutron transmutation doping, can be considered the most important one for semiconductors. Experimental and theoretical research exploiting the differences in all the properties has been conducted and will be illustrated with selected examples. Manuel Cardona, the longtime editor-in-chief of solid state communications has been and continues to be one of the major contributors to this field of solid state physics and it is a great pleasure to dedicate this review to him.     

Quantum coherence dynamics of spin pairs in many-spin cluster

We consider the dynamics of a quantum coherence of two chosen spins in systems of dipolar coupled nuclear spins s=1/2 in solid. With the purpose to study this coherence we suggest two different methods. One of them uses the partial trace technique and reduced density matrix. The second method is based on the calculation the intensity of multiple quantum coherences using two-spin operator and the density matrix of the whole spin system. Results of calculations of the multiple-quantum dynamics in spin clusters of various dimensionalities are presented. It is shown that the whole density matrix method is more informative than the method based on the reduced density matrix.     

Statistical physics of human beings in games:Controlled experiments

It is important to know whether the laws or phenomena in statistical physics for natural systems with non-adaptive agents still hold for social human systems with adaptive agents, because this implies whether it is possible to study or understand social human systems by using statistical physics originating from natural systems. For this purpose, we review the role of human adaptability in four kinds of specific human behaviors, namely, normal behavior, herd behavior, contrarian behavior, and hedge behavior. The approach is based on controlled experiments in the framework of market-directed resource-allocation games. The role of the controlled experiments could be at least two-fold: adopting the real human decision-making process so that the system under consideration could reflect the performance of genuine human beings;making it possible to obtain macroscopic physical properties of a human system by tuning a particular factor of the system,thus directly revealing cause and effect. As a result, both computer simulations and theoretical analyses help to show a few counterparts of some laws or phenomena in statistical physics for social human systems: two-phase phenomena or phase transitions, entropy-related phenomena, and a non-equilibrium steady state. This review highlights the role of human adaptability in these counterparts, and makes it possible to study or understand some particular social human systems by means of statistical physics coming from natural systems.     

Nuclear spin relaxation induced by a mechanical resonator

We report on measurements of the spin lifetime of nuclear spins strongly coupled to a micromechanical cantilever as used in magnetic resonance force microscopy. We find that the rotating-frame correlation time of the statistical nuclear polarization is set by the magnetomechanical noise originating from the thermal motion of the cantilever. Evidence is based on the effect of three parameters: (1) the magnetic field gradient (the coupling strength), (2) the Rabi frequency of the spins (the transition energy), and (3) the temperature of the low-frequency mechanical modes. Experimental results are compared to relaxation rates calculated from the spectral density of the magnetomechanical noise.     

Study of Low Temperature Magnetic Properties of a Single Chain Magnet with Alternate Isotropic and Non-collinear Anisotropic Units

Here we study thermodynamic properties of an important class of single-chain magnets (SCMs), where alternate units are isotropic and anisotropic with anisotropy axes being non-collinear. This class of SCMs shows slow relaxation at low temperatures which results from the interplay of two different relaxation mechanisms, namely dynamical and thermal. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. We here show how statistical behavior of this class of SCMs can be studied using a transfer matrix (TM) method. We also, for the first time, discuss in detail how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. At the end of this paper, we apply this technique to study a real helical chain magnet.     

Impact of the monetary crisis on statistical properties of the Jakarta and Kuala Lumpur stock exchange indices

Using the tools developed for statistical physics, we simultaneously analyze statistical properties of the Jakarta and Kuala Lumpur Stock Exchange indices. In spite of the small number of the data used in the analysis, the result still shows the universal behavior of complex systems previously found in the leading stock indices. We also analyze their properties before and after the crash caused by the monetary crisis. To locate the time position when the crash started we use the Omori law. We found that after the crash both stocks do not show a same statistical behavior. The impact of currency controls is observed in the distribution of the index returns.     

Universal Long-Time Relaxation on 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.     

Nuclear physics and ideas of quantum chaos

The field nowadays called “many-body quantum chaos” was started in 1939 with the article by I.I. Gurevich studying the regularities of nuclear spectra. The field has been extensively developed recently, both mathematically and in application to mesoscopic systems and quantum fields. We argue that nuclear physics and the theory of quantum chaos are mutually beneficial. Many ideas of quantum chaos grew up from the factual material of nuclear physics; this enrichment still continues to take place. On the other hand, many phenomena in nuclear structure and reactions, as well as the general problem of statistical physics of finite strongly interacting systems, can be understood much deeper with the help of ideas and methods borrowed from the field of quantum chaos. A brief review of the selected topics related to the recent development is presented.     

Signature of the ferromagnetic (T = 0) transition in real space and time

A detailed study of the spatio-temporal dynamics in several Hubbard clusters at zero temperature is performed. Small systems of two and three electrons, which could be considered representative systems of Nagaoka's, Mielke's and Tasaki's ferromagnetism, are investigated using a combination of analytical and numerical exact diagonalization techniques. The results raise the possibility that spin-dependent localization is correlated in real space and real time with the transition to a saturated ferromagnetic state. The long-time average of the expectation value of the center of mass coordinates for electrons with spin up does not coincide with that for electrons with spin down at the transition. The reason for this is that the long-time averages of the probabilities are different for states in which the spins of one system are exchanged with another. The physical origin of itinerant ferromagnetism is discussed.     

Integro-differential equation for joint probability density in phase space associated with continuous-time random walk

We derive an integro-differential equation for the joint probability density function in phase space associated with the continuous-time random walk, with generic waiting time probability density function and external force. This equation permits us to investigate whole diffusion processes covering initial-, intermediate-, and long-time ranges, which can distinguish the evolution details for systems having the same behavior in the long-time limit with different initial- and intermediate-time behaviors. Moreover, we obtained analytic solutions for probability density functions both in velocity and phase spaces, and interesting dynamic behaviors are discovered.