arXiv subjects
Publications and source records attributed to Seiji Miyashita.
This paper presents studies on a deterministic annealing algorithm based on quantum annealing for variational Bayes (QAVB) inference, which can be seen as an extension of the simulated annealing for variational Bayes (SAVB) inference. QAVB is as easy as SAVB to implement. Experiments revealed QAVB finds a better local optimum than SAVB in terms of the variational free energy in latent Dirichlet allocation (LDA).
The unusual thermodynamic properties of the Ising antiferromagnet supplemented with a ferromagnetic, mean-field term are outlined. This simple model is inspired by more realistic models of spin-crossover materials. The phase diagram is estimated using Metropolis Monte Carlo methods, and differences with preliminary Wang-Landau Monte Carlo results for small systems are noted.
We consider the interacting Bessel processes, a family of multiple-particle systems in one dimension where particles evolve as individual Bessel processes and repel each other via a log-potential. We consider two limiting regimes for this family on its two main parameters: the inverse temperature beta and the Bessel index nu. We obtain the time-scaled steady-state distributions of the processes for the cases where beta or nu are large but finite. In particular, for large beta we show that the steady-state distribution of the system corresponds to the eigenvalue distribution of the beta-Laguerre ensembles of random matrices. We also estimate the relaxation time to the steady state in both cases. We find that in the freezing regime beta->infinity, the scaled final positions of the particles are locked at the square root of the zeroes of the Laguerre polynomial of parameter nu-1/2 for any initial configuration, while in the regime nu->infinity, we prove that the scaled final positions of the particles converge to a single point. In order to obtain our results, we use the theory of Dunkl operators, in particular the intertwining operator of type B. We derive a previously unknown expression for this operator and study its behaviour in both limiting regimes. By using these limiting forms of the intertwining operator, we derive the steady-state distributions, the estimations of the relaxation times and the limiting behaviour of the processes.
We study non-equilibrium stationary states of a cavity system consisting of many atoms interacting with a quantized cavity field mode, under a driving field in a dissipative environment. We derive a quantum master equation which is suitable for treating systems with a strong driving field and a strong atom-photon interaction. We do this by making use of the fact that the mean-field dynamics are exact in the thermodynamic limit thanks to a uniform coupling between atoms and photons. We find ordered states with symmetry-broken components of the photon field and atomic excitation driven by the external field. The mechanism by which these ordered states arise is discussed from the viewpoint of the quantum interference effect.
We developed a new quantum annealing (QA) algorithm for Dirichlet process mixture (DPM) models based on the Chinese restaurant process (CRP). QA is a parallelized extension of simulated annealing (SA), i.e., it is a parallel stochastic optimization technique. Existing approaches [Kurihara et al. UAI2009, Sato et al. UAI2009] and cannot be applied to the CRP because their QA framework is formulated using a fixed number of mixture components. The proposed QA algorithm can handle an unfixed number of classes in mixture models. We applied QA to a DPM model for clustering vertices in a network where a CRP seating arrangement indicates a network partition. A multi core processor was used for running QA in experiments, the results of which show that QA is better than SA, Markov chain Monte Carlo inference, and beam search at finding a maximum a posteriori estimation of a seating arrangement in the CRP. Since our QA algorithm is as easy as to implement the SA algorithm, it is suitable for a wide range of applications.
Magnetism in SmPd2Al3 was investigated on a single crystal by magnetometry and neutron diffraction. SmPd2Al3 represents a distinctive example of the Sm magnetism exhibiting complex magnetic behavior at low temperatures with four consecutive magnetic phase transitions at 3.4, 3.9, 4.3 and 12.5 K. The rich magnetic phase diagram of this compound reflects the specific features of the Sm3+ ion, namely the energy nearness of the ground-state multiplet J = 5/2 and the first excited multiplet J = 7/2 in conjunction with strong crystal field influence. Consequently, a significantly reduced Sm magnetic moment in comparison with the theoretical Sm3+ free-ion value is observed. Despite the strong neutron absorption by natural samarium and the small Sm magnetic moment (~ 0.2 μB) we have successfully determined the magnetic k-vector (1/3, 1/3, 0) of the phase existing in the temperature interval 12.5 - 4.3 K. This observation classifies the SmPd2Al3 compound as a magnetically frustrated system. The complex magnetic behavior of this material is further illustrated by kinetic effects of the magnetization inducing rather complicated magnetic structure with various metastable states.
The decoherence of a quantum system $S$ coupled to a quantum environment $E$ is considered. For states chosen uniformly at random from the unit hypersphere in the Hilbert space of the closed system $S+E$ we derive a scaling relationship for the sum of the off-diagonal elements of the reduced density matrix of $S$ as a function of the size $D_E$ of the Hilbert space of $E$. This sum decreases as $1/\sqrt{D_E}$ as long as $D_E\gg 1$. This scaling prediction is tested by performing large-scale simulations which solve the time-dependent Schr{ö}dinger equation for a ring of spin-1/2 particles, four of them belonging to $S$ and the others to $E$. Provided that the time evolution drives the whole system from the initial state toward a state which has similar properties as states belonging to the class of quantum states for which we derived the scaling relationship, the scaling prediction holds. For systems which do not exhibit this feature, it is shown that increasing the complexity (in terms of connections) of the environment or introducing a small amount of randomness in the interactions in the environment suffices to observe the predicted scaling behavior.
The intensity of electron spin resonance (ESR) of the nanoscale molecular magnet V15 is studied. We calculate the temperature dependence of the intensity at temperatures from high to low. In particular, we find that the low-temperature ESR intensity is significantly affected by the Dzyaloshinsky-Moriya interaction.
The Calogero-Moser systems are a series of interacting particle systems on one dimension that are both classically and quantum-mechanically integrable. Their integrability has been established through the use of Dunkl operators (a series of differential-difference operators that depend on the choice of an abstract set of vectors, or root system). At the same time, Dunkl operators are used to define a family of stochastic processes called Dunkl processes. We showed in a previous paper that when the coupling constant of interaction of the symmetric Dunkl process on the root system A(N-1) goes to infinity (the freezing regime), its final configuration is proportional to the roots of the Hermite polynomials. It is also known that the positions of the particles of the Calogero-Moser system with particle exchange become fixed at the roots of the Hermite polynomials in the freezing regime. Although both systems present a freezing behaviour that depends on the roots of the Hermite polynomials, the reason for this similarity has been an open problem until now. In the present work, we introduce a new type of similarity transformation called the diffusion-scaling transformation, in which a new space variable is given by a diffusion-scaling variable constructed using the original space and time variables. We prove that the abstract Calogero-Moser system on an arbitrary root system is a diffusion-scaling transform of the Dunkl process on the same root system. With this, we prove that the similar freezing behaviour of the two systems on A(N-1) stems from their similar mathematical structure.
It is demonstrated that the canonical distribution for a subsystem of a closed system follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. It is shown that this conclusion holds for both integrable or nonintegrable systems even though the whole system may contain as little as a few thousand particles. In other words, we demonstrate that the canonical distribution holds for subsystems of experimentally relevant sizes and observation times.
We consider a one-dimensional system of Brownian particles that repel each other through a logarithmic potential. We study two formulations for the system and the relation between them. The first, Dyson's Brownian motion model, has an interaction coupling constant determined by the parameter beta > 0. When beta = 1,2 and 4, this model can be regarded as a stochastic realization of the eigenvalue statistics of Gaussian random matrices. The second system comes from Dunkl processes, which are defined using differential-difference operators (Dunkl operators) associated with finite abstract vector sets called root systems. When the type-A root system is specified, Dunkl processes constitute a one-parameter system similar to Dyson's model, with the difference that its particles interchange positions spontaneously. We prove that the type-A Dunkl processes with parameter k > 0 starting from any symmetric initial configuration are equivalent to Dyson's model with the parameter beta = 2k. We focus on the intertwining operators, since they play a central role in the mathematical theory of Dunkl operators, but their general closed form is not yet known. Using the equivalence between symmetric Dunkl processes and Dyson's model, we extract the effect of the intertwining operator of type A on symmetric polynomials from these processes' transition probability densities. In the strong coupling limit, the intertwining operator maps all symmetric polynomials onto a function of the sum of their variables. In this limit, Dyson's model freezes, and it becomes a deterministic process with a final configuration proportional to the roots of the Hermite polynomials multiplied by the square root of the process time, while being independent of the initial configuration.
It has previously been pointed out that the coexistence of infinite-range and short-range interactions causes a system to have a phase transition of the mean-field universality class, in which the cluster size is finite even at the critical point. In the present paper, we study this property in a model of bistable molecules, whose size changes depending on the bistable states. The molecules can move in space, interacting via an elastic interaction. It is known that due to the different sizes, an effective long-range interaction between the spins appears, and thus this model has a mean-field type of phase transition. It is found that the scaling properties of the shift of the critical temperature from the pure short-range limit in the model with infinite-range and short-range interactions hold also in the present model, regarding the ratio of the size of the two states as a control parameter for the strength of the long-range interaction. By studying the structure factor, it is shown that the dependence of the cluster size at the critical temperature also shows the same scaling properties as a previously studied model with both infinite-range and short-range interactions. We therefore conclude that these scaling relations hold universally in hybrid models with both short-range and weak long-range interactions.
Nucleation, commonly associated with discontinuous transformations between metastable and stable phases, is crucial in fields as diverse as atmospheric science and nanoscale electronics. Traditionally, it is considered a microscopic process (at most nano-meter), implying the formation of a microscopic nucleus of the stable phase. Here we show for the first time, that considering long-range interactions mediated by elastic distortions, nucleation can be a macroscopic process, with the size of the critical nucleus proportional to the total system size. This provides a new concept of "macroscopic barrier-crossing nucleation". We demonstrate the effect in molecular dynamics simulations of a model spin-crossover system with two molecular states of different sizes, causing elastic distortions.
Recently, it has been found that an effective long-range interaction is realized among local bistable variables (spins) in systems where the elastic interaction causes ordering of the spins. In such systems, generally we expect both long-range and short-range interactions to exist. In the short-range Ising model, the correlation length diverges at the critical point. In contrast, in the long-range interacting model the spin configuration is always uniform and the correlation length is zero. As long as a system has non-zero long-range interactions, it shows criticality in the mean-field universality class, and the spin configuration is uniform beyond a certain scale. Here we study the crossover from the pure short-range interacting model to the long-range interacting model. We investigate the infinite-range model (Husimi-Temperley model) as a prototype of this competition, and we study how the critical temperature changes as a function of the strength of the long-range interaction. This model can also be interpreted as an approximation for the Ising model on a small-world network. We derive a formula for the critical temperature as a function of the strength of the long-range interaction. We also propose a scaling form for the spin correlation length at the critical point, which is finite as long as the long-range interaction is included, though it diverges in the limit of the pure short-range model. These properties are confirmed by extensive Monte Carlo simulations.
We study the time evolution of the reduced density matrix of a system of spin-1/2 particles interacting with an environment of spin-1/2 particles. The initial state of the composite system is taken to be a product state of a pure state of the system and a pure state of the environment. The latter pure state is prepared such that it represents the environment at a given finite temperature in the canonical ensemble. The state of the composite system evolves according to the time-dependent Schr{ö}dinger equation, the interaction creating entanglement between the system and the environment. It is shown that independent of the strength of the interaction and the initial temperature of the environment, all the eigenvalues of the reduced density matrix converge to their stationary values, implying that also the entropy of the system relaxes to a stationary value. We demonstrate that the difference between the canonical density matrix and the reduced density matrix in the stationary state increases as the initial temperature of the environment decreases. As our numerical simulations are necessarily restricted to a modest number of spin-1/2 particles ($<36$), but do not rely on time-averaging of observables nor on the assumption that the coupling between system and environment is weak, they suggest that the stationary state of the system directly follows from the time evolution of a pure state of the composite system, even if the size of the latter cannot be regarded as being close to the thermodynamic limit.
We introduce an event-based corpuscular simulation model that reproduces the wave mechanical results of single-photon double slit and two-beam interference experiments and (of a one-to-one copy of an experimental realization) of a single-photon interference experiment with a Fresnel biprism. The simulation comprises models that capture the essential features of the apparatuses used in the experiment, including the single-photon detectors recording individual detector clicks. We demonstrate that incorporating in the detector model, simple and minimalistic processes mimicking the memory and threshold behavior of single-photon detectors is sufficient to produce multipath interference patterns. These multipath interference patterns are built up by individual particles taking one single path to the detector where they arrive one-by-one. The particles in our model are not corpuscular in the standard, classical physics sense in that they are information carriers that exchange information with the apparatuses of the experimental set-up. The interference pattern is the final, collective outcome of the information exchanges of many particles with these apparatuses. The interference patterns are produced without making reference to the solution of a wave equation and without introducing signalling or non-local interactions between the particles or between different detection points on the detector screen.
We study how the degree of ordering depends on the strength of the thermal and quantum fluctuations in frustrated systems by investigating the correlation function of the order parameter. Concretely, we compare the equilibrium spin correlation function in a frustrated lattice which exhibits a non-monotonic temperature dependence (reentrant type dependence) with that in the ground state as a function of the transverse field that causes the quantum fluctuation. We find the correlation function in the ground state also shows a non-monotonic dependence on the strength of the transverse field. We also study the real-time dynamics of the spin correlation function under a time-dependent field. After sudden decrease of the temperature, we found non-monotonic changes of the correlation function reflecting the static temperature dependence, which indicates that an effective temperature of the system changes gradually. For the quantum system, we study the dependence of changes of the correlation function on the sweeping speed of the transverse field. Contrary to the classical case, the correlation function varies little in a rapid change of the field, though it shows a non-monotonic change when we sweep the field slowly.
We study ordering mechanisms which are induced by the quantum fluctuation in fully frustrated Ising spin systems. Since there are many degenerated states in frustrated systems, "order by thermal disorder" often takes place due to a kind of entropy effect. To consider "order by quantum disorder" in fully frustrated Ising spin systems, we apply transverse field as quantum fluctuation. There exists a ferromagnetic correlation in each sublattice. The sublattice correlation at zero temperature is enlarged due to transverse field. The quantum fluctuation enhances the solid order at zero temperatures. This is an example of quantum field induced ordering in fully frustrated systems. We also study a case in which the transverse field induces a reentrant behavior as another type of order by quantum disorder, and compare correspondent cases in the classical systems.