arXiv subjects

Tetsuo Deguchi

Publications and source records attributed to Tetsuo Deguchi.

At least 19 recordsLinked to original sources

arXiv2026

Random knotting in very long off-lattice self-avoiding polygons

We present experimental results on knotting in off-lattice self-avoiding polygons in the bead-chain model. Using Clisby's tree data structure and the scale-free pivot algorithm, for each $k$ between $10$ and $27$ we generated $2^{43-k}$ polygons of size $n=2^k$. Using a new knot diagram simplification and invariant-free knot classification code, we were able to determine the precise knot type of each polygon. The results show that the number of prime summands of knot type $K$ in a random $n$-gon is very well described by a Poisson distribution. We estimate the characteristic length of knotting as $656500 \pm 2500$. We use the count of summands for large $n$ to measure knotting rates and amplitude ratios of knot probabilities more accurately than previous experiments. Our calculations agree quite well with previous on-lattice computations, and support both knot localization and the knot entropy conjecture.

cond-mat.stat-mech↗

arXiv2025

Effects of multiple cycles on the resistance distance of a strand in a homogeneous polymer network

We show that the resistance distance between a pair of adjacent vertices in a phantom network generated randomly by a Monte-Carlo method depends on the existence of short cycles around it. Here we assume that phantom networks have no fixed points but their centers of mass are located at a point. The resistance distance corresponds to the mean-square deviation of the end-to-end vector along the strand connecting the adjacent vertices. We generate random networks with fixed valency $f$ but different densities of short cycles via a Metropolis method that rewires edges among four vertices chosen randomly. In the process the cycle rank is conserved. However, the densities of short cycles are determined by the rate of randomization $kT$ which appears in the acceptance ratio $\exp(-\Delta U/kT)$ of rewiring. If a strand has few short cycles around itself, the mean squared deviation of the strand is equal to $2/f$. If it is part of a short cycle, i.e., the network has a short loop which consists of a sequence of strands including the given strand itself, its resistance distance is smaller than $2/f$, while if it is not included in a cycle but adjacent to cycles, its resistance distance is larger than $2/f$. We show it via an electrical circuit analogy of the network. Moreover, we numerically show that the effect of multiple cycles on the resistance distance is expressed as a linear combination of the effects of isolated single cycles. It follows that cycles independently have an effect on the fluctuation properties of a strand in a polymer network.

cond-mat.soft↗

arXiv2025

An exact formula for the contraction factor of a subdivided Gaussian topological polymer

We consider the radius of gyration of a Gaussian topological polymer $G$ formed by subdividing a graph $G'$ of arbitrary topology (for instance, branched or multicyclic). We give a new exact formula for the expected radius of gyration and contraction factor of $G$ in terms of the number of subdivisions of each edge of $G'$ and a new weighted Kirchhoff index for $G'$. The formula explains and extends previous results for the contraction factor and Kirchhoff index of subdivided graphs.

cond-mat.stat-mech↗

arXiv2024

Simulating phase inversion processes by coupled map lattice: Towards the theoretical design of food texture and quality in dairy processing from fresh cream to butter via whipped cream

We present a theoretical model and simulation for the formation dynamics of diverse texture patterns that emerge spontaneously or self-organize during phase inversion processes of fresh cream by mechanical whipping. The results suggest that the model should be applied for theoretically designing the texture and quality of whipped cream and butter products. The modeling complexity in phase inversion processes from fresh cream via whipped cream to butter was overcome by using a well-established complex systems approach, coupled map lattice (CML). The proposed CML consists of a minimal set of procedures (i.e., parameterized nonlinear maps), whipping, coalescence, and flocculation, acting on the appropriately coarse-grained field variables, surface energy, cohesive energy, and velocity (flow) of the emulsion defined on a two-dimensional square lattice. In the CML simulations, two well-known and different phase inversion processes are reproduced at high and low whipping temperatures. The overrun and viscosity changes simulated in these processes are at least qualitatively consistent with those observed in experiments. We characterize these processes exhibiting different texture patterns as the viscosity dominance at high whipping temperature and as the overrun dominance at low whipping temperature on the viscosity-overrun plane, which is one of the state diagrams.

cond-mat.soft↗

arXiv2024

Exact Bethe quantum numbers of the massive XXZ chain in the two down-spin sector

Every solution of the Bethe ansatz equations (BAE) is characterized by a set of quantum numbers called the Bethe quantum numbers, which are fundamental for evaluating it numerically. We rigorously derive the Bethe quantum numbers for the real solutions of the spin-1/2 massive XXZ spin chain in the two down-spin sector, assuming the existence of solutions to some form of BAE. In the sector the quantum numbers $J_1$ and $J_2$ were derived for complex solutions, but not for real solutions. We show the exact results in the sector as follows. (\si) When two Bethe quantum numbers are different, i.e., for $J_1 \ne J_2$, we introduce a graphical method, which we call a contour method, for deriving the solution of BAE to a given set of Bethe quantum numbers. By the method, we can readily show the existence and the uniqueness of the solution. (\sii) When two Bethe quantum numbers are equal, i.e. for $J_1 = J_2$, we derive the criteria for the collapse of two-strings and the emergence of an extra two-string by an analytic method. (\siii) We obtain the number of real solutions, which depends on the site number $N$ and the XXZ anisotropy parameter $\zeta$. (\siv) We derive all infinite-valued solutions of BAE for the XXX spin chain in the two down-spin sector through the XXX limit. (\sv) We explicitly show the completeness of the Bethe ansatz in terms of the Bethe quantum numbers.

math-ph↗

arXiv2024

Dynamical toy model of interacting $N$ agents robustly exhibiting Zipf's law

We propose a dynamical toy model of agents which possess a quantity and have an interaction radius depending on the amount of the quantity. They exchange the quantity with agents existing within their interaction radii. It is shown in the paper that the distribution of the quantity of agents is robustly governed by Zipf's law for a small density of agents independent of the number of agents and the type of interaction, despite the simplicity of the rules. The model can exhibit other power laws with different exponents and the Gaussian distributions. The difference in the mechanism underlying Zipf's law and other power laws are studied by mapping the systems into graphs and investigating quantities characterizing the mapped graph. Thus, this model suggests one of the origins of Zipf's law, i.e., the most common fundamental characteristics necessary for Zipf's law to appear.

physics.soc-ph↗

arXiv2022

Dynamics of quantum double dark-solitons and an exact finite-size scaling of Bose-Einstein condensation

We show several novel aspects in the exact non-equilibrium dynamics of quantum double dark-soliton states in the Lieb-Liniger model for the one-dimensional Bose gas with repulsive interactions. We also show an exact finite-size scaling of the fraction of the Bose-Einstein condensation (BEC) in the ground state, which should characterize the quasi-BEC in quantum double dark-soliton states that we assume to occur in the weak coupling regime. First, we show the exact time evolution of the density profile in the quantum state associated with a quantum double dark-soliton by the Bethe ansatz. Secondly, we derive a kind of macroscopic quantum wave-function effectively by exactly evaluating the square amplitude and phase profiles of the matrix element of the field operator between the quantum double dark-soliton states. The profiles are close to those of dark-solitons particularly in the weak-coupling regime. Then, the scattering of two notches in the quantum double dark-soliton state is exactly demonstrated. It is suggested from the above observations that the quasi-BEC should play a significant role in the dynamics of quantum double dark-soliton states. If the condensate fraction is close to 1, the quantum state should be well approximated by the quasi-BEC state where the mean-field picture is valid.

cond-mat.quant-gas↗

arXiv2022

Random graph embeddings with general edge potentials

In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects, Lennard-Jones potentials, bending energies, and other physically realistic models. A configuration of $n$ monomers in $\mathbb{R}^d$ can be written as a collection of $d$ coordinate vectors, each in $\mathbb{R}^n$. Our first main result is that entries from different coordinate vectors are uncorrelated, even when they are different coordinates of the same monomer. We predict that this property holds in realistic simulations and in actual polymer configurations (in the absence of an external field). Our second main contribution is a theorem explaining when and how a probability distribution on embeddings of a complicated graph may be pushed forward to a distribution on embeddings of a simpler graph to aid in computations. This construction is based on the idea of chain maps in homology theory. We use it to give a new formula for edge covariances in phantom network theory and to compute some expectations for a freely-jointed network.

cond-mat.stat-mech↗

arXiv2021

Quantum dark solitons in the 1D Bose gas: From single to double dark-solitons

We study quantum double dark-solitons by constructing corresponding quantum states in the Lieb-Liniger model for the one-dimensional Bose gas. Here we expect that the Gross-Pitaevskii (GP) equation should play a central role in the long distance mean-field behavior of the 1D Bose gas. We first introduce novel quantum states of a single dark soliton with a nonzero winding number. We show them by exactly evaluating not only the density profile but also the profiles of the square amplitude and phase of the matrix element of the field operator between the $N$-particle and $(N-1)$-particle states. For elliptic double dark-solitons, the density and phase profiles of the corresponding states almost perfectly agree with those of the classical solutions, respectively, in the weak coupling regime. We then show that the scheme of the mean-field product state is quite effective for the quantum states of double dark solitons. Assigning the ideal Gaussian weights to a sum of the excited states with two particle-hole excitations we obtain double dark-solitons of distinct narrow notches with different depths. We suggest that the mean-field product state should be well approximated by the ideal Gaussian weighted sum of the low excited states with a pair of particle-hole excitations. The results of double dark-solitons should be fundamental and useful for constructing quantum multiple dark-solitons.

cond-mat.quant-gas↗

arXiv2020

Radius of Gyration, Contraction Factors, and Subdivisions of Topological Polymers

We consider the topologically constrained random walk model for topological polymers. In this model, the polymer forms an arbitrary graph whose edges are selected from an appropriate multivariate Gaussian which takes into account the constraints imposed by the graph type. We recover the result that the expected radius of gyration can be given exactly in terms of the Kirchhoff index of the graph. We then consider the expected radius of gyration of a topological polymer whose edges are subdivided into $n$ pieces. We prove that the contraction factor of a subdivided polymer approaches a limit as the number of subdivisions increases, and compute the limit exactly in terms of the degree-Kirchhoff index of the original graph. This limit corresponds to the thermodynamic limit in statistical mechanics and is fundamental in the physics of topological polymers. Furthermore, these asymptotic contraction factors are shown to fit well with molecular dynamics simulations.

cond-mat.stat-mech↗

arXiv2020

Factoring the Laplacian to understand topological polymers

A ring polymer is a random walk whose steps obey a single linear condition; their sum vanishes. Factoring the graph Laplacian into the product of the incidence matrix and its transpose allows us to show that for a more complicated network, the steps must lie in a linear subspace determined by the graph topology. This provides a useful new perspective on the James--Guth theory of phantom elastic networks. In particular, we formulate phantom networks which are free from the constraints of fixed crosslinks. For a given network the solution of the loop constraints makes the partition function finite-valued in the path integral formulation without applying any external forces or fixing any monomer positions. The resulting probability distribution on edge displacements is rotationally invariant, which is practically quite useful for generating unbiased random samples of edge displacements and monomer positions. Furthermore, one can exactly calculate many physical quantities such as correlation functions with respect to this distribution. Finally, this reformulation lends itself well to the case of non-Gaussian distributions. We illustrate this by computing the expected radius of gyration of a ring polymer in a wide variety of models.

cond-mat.stat-mech↗

arXiv2019

Universal scrambling in gapless quantum spin chains

Information scrambling, characterized by the out-of-time-ordered correlator (OTOC), has attracted much attention, as it sheds new light on chaotic dynamics in quantum many-body systems. The scale invariance, which appears near the quantum critical region in condensed matter physics, is considered to be important for the fast decay of the OTOC. In this paper, we focus on the one-dimensional spin-1/2 XXZ model, which exhibits quantum criticality in a certain parameter region, and investigate the relationship between scrambling and the scale invariance. We quantify scrambling by the averaged OTOC over the Pauli operator basis, which is related to the operator space entanglement entropy (OSEE). Using the infinite time-evolving block decimation (iTEBD) method, we numerically calculate time dependence of the OSEE in the early time region in the thermodynamic limit. We show that the averaged OTOC decays faster in the gapless region than in the gapped region. In the gapless region, the averaged OTOC behaves in the same manner regardless of the anisotropy parameter. This result is consistent with the fact that the low energy excitations of the gapless region belong to the same universality class as the Tomonaga-Luttinger liquid with the central charge c = 1. Furthermore, we estimate c by fitting the numerical data of the OSEE with an analytical result of the two-dimensional conformal field theory, and confirmed that c is close to unity. Thus, our numerical results suggest that the scale invariance is crucial for the universal behavior of the OTOC.

cond-mat.stat-mech↗

arXiv2018

Exact regimes of collapsed and extra two-string solutions in the two down-spin sector of the spin-1/2 massive XXZ spin chain

We derive exactly the number of complex solutions with two down-spins in the massive regime of the periodic spin-1/2 XXZ spin chain of $N$ sites. Here we remark that every solution of the Bethe ansatz equations is characterized by a set of quantum numbers. We derive them analytically for all the complex solutions in the sector, which we call two-string solutions. We show that in a region of $N$ and $Δ$ the number of two-string solutions is by two larger than the number due to the string hypothesis, i.e., an extra pair of two-strings appears. We determine it exactly and also such regions where $m$ two-string solutions collapse for any positive integers $m$. We illustrate the extra and standard two-string solutions numerically. In the sector we show that the string deviations are exponentially small with respect to $N$ if $N$ is large. We argue that for any finite solution of the spin-1/2 XXX chain there is such a solution of the spin-1/2 XXZ chain that has the same quantum numbers in common with the XXX solution.

cond-mat.stat-mech↗

arXiv2018

Finite-size scaling with respect to interaction and disorder strength at the many-body localization transition

We present a finite-size scaling for both interaction and disorder strengths in the critical regime of the many-body localization (MBL) transition for a spin-1/2 XXZ spin chain with a random field by studying level statistics. We show how the dynamical transition from the thermal to MBL phase depends on interaction together with disorder by evaluating the ratio of adjacent level spacings, and thus, extend previous studies in which interaction coupling is fixed. We introduce an extra critical exponent in order to describe the nontrivial interaction dependence of the MBL transition. It is characterized by the ratio of the disorder strength to the power of the interaction coupling with respect to the extra critical exponent and not by the simple ratio between them.

cond-mat.dis-nn↗

arXiv2017

Knotting probability of self-avoiding polygons under a topological constraint

We define the knotting probability of a knot $K$ by the probability for a random polygon (RP) or self-avoiding polygon (SAP) of $N$ segments having the knot type $K$. We show fundamental and generic properties of the knotting probability particularly its dependence on the excluded volume. We investigate them for the SAP consisting of hard cylindrical segments of unit length and radius $r_{\rm ex}$. For various prime and composite knots we numerically show that a compact formula describes the knotting probabilities for the cylindrical SAP as a function of segment number $N$ and radius $r_{\rm ex}$. It connects the small-$N$ to the large-$N$ behavior and even to lattice knots in the case of large values of radius. As the excluded volume increases the maximum of the knotting probability decreases for prime knots except for the trefoil knot. If it is large, the trefoil knot and its descendants are dominant among the nontrivial knots in the SAP. From the factorization property of the knotting probability we derive a relation among the estimates of a fitting parameter for all prime knots, which suggests the local knot picture. Here we remark that the cylindrical SAP gives a model of circular DNA which are negatively charged and semiflexible, where radius $r_{\rm ex}$ corresponds to the screening length.

cond-mat.soft↗

arXiv2017

Scaling behavior of knotted random polygons and self-avoiding polygons: Topological swelling with enhanced exponent

We show that the average size of self-avoiding polygons (SAP) with a fixed knot is much larger than that of no topological constraint if the excluded volume is small and the number of segments is large. We call it topological swelling. We argue an "enhancement" of the scaling exponent for random polygons with a fixed knot. We study them systematically through SAP consisting of hard cylindrical segments with various different values of the radius of segments. Here we mean by the average size the mean-square radius of gyration. Furthermore, we show numerically that the equilibrium length of a composite knot is given by the sum of those of all constituent prime knots. Here we define the equilibrium length of a knot by such a number of segments that topological entropic repulsions are balanced with the knot complexity in the average size. The additivity suggests the local knot picture.

cond-mat.soft↗

arXiv2016

Statistical and hydrodynamic properties of topological polymers for various graphs showing enhanced short-range correlation

For various polymers with different topological structures we numerically evaluate the mean-square radius of gyration and the hydrodynamic radius systematically through simulation. We call polymers with nontrivial topology topological polymers. We evaluate the two quantities both for ideal and real chain models and show that the ratios of the quantities among different topological types do not depend on the existence of excluded volume if the topological polymers have only up to trivalent vertices, as far as the polymers investigated. We also evaluate the ratio of the gyration radius to the hydrodynamic radius, which we expect to be universal from the viewpoint of renormalization group. Furthermore, we show that the short-distance intrachain correlation is much enhanced for topological polymers expressed with complex graphs.

cond-mat.soft↗

arXiv2016

Quantum states of dark solitons in the 1D Bose gas

We present a series of quantum states that are characterized by dark solitons of the nonlinear Schrödinger equation (i.e. the Gross-Pitaevskii equation) for the one-dimensional (1D) Bose gas interacting through the repulsive delta-function potentials. The classical solutions satisfy the periodic boundary conditions and we call them periodic dark solitons. Through exact solutions we show corresponding aspects between the states and the solitons in the weak coupling case: the quantum and classical density profiles completely overlap with each other not only at an initial time but also at later times over a long period of time, and they move together with the same speed in time; the matrix element of the bosonic field operator between the quantum states has exactly the same profiles of the square amplitude and the phase as the classical complex scalar field of a periodic dark soliton not only at the initial time but also at later times, and the corresponding profiles move together for a long period of time. We suggest that the corresponding properties hold rigorously in the weak coupling limit. Furthermore, we argue that the lifetime of the dark soliton-like density profile in the quantum state becomes infinitely long as the coupling constant approaches zero, by comparing it with the quantum speed limit time. Thus, we call the quantum states quantum dark soliton states.

cond-mat.quant-gas↗