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Akira Shimizu

Publications and source records attributed to Akira Shimizu.

At least 37 records · Page 2Linked to original sources
arXiv2015

Liquid is More Rigid than Solid in a High-Frequency Region

We compare rigidity of materials in two phases, liquid and solid phases. As a measure of the rigidity, we employ the one characterizing how firmly the material is fixed by low density of pinning centers, such as impurities and rough surfaces of walls, against a weak force. Although a solid is more rigid than a liquid against a low-frequency force, we find that against a high-frequency force the liquid becomes more rigid than the solid of the same material. Since this result is derived from universal properties of a response function, it is valid for wide classes of materials, including quantum and classical systems and crystalline and amorphous solids. An instructive example is studied using nonequilibrium molecular dynamics simulations. We find that the frequency region in which a solid is more flexible than a liquid is not purely determined by intrinsic properties of the solid. It depends also on extrinsic factors such as the density of pinning centers.

cond-mat.stat-mech↗
arXiv2014

Thermal Pure Quantum States of Many-Particle Systems

We generalize the thermal pure quantum (TPQ) formulation of statistical mechanics, in such a way that it is applicable to systems whose Hilbert space is infinite dimensional. Assuming particle systems, we construct the grand-canonical TPQ (gTPQ) state, which is the counterpart of the grand-canonical Gibbs state of the ensemble formulation. A single realization of the gTPQ state gives all quantities of statistical-mechanical interest, with exponentially small probability of error. This formulation not only sheds new light on quantum statistical mechanics but also is useful for practical computations. As an illustration, we apply it to the Hubbard model, on a one-dimensional (1d) chain and on a two-dimensional (2d) triangular lattice. For the 1d chain, our results agree well with the exact solutions over wide ranges of temperature, chemical potential and the on-site interaction. For the 2d triangular lattice, for which exact results are unknown, we obtain reliable results over a wide range of temperature. We also find that finite-size effects are much smaller in the gTPQ state than in the canonical TPQ (cTPQ) state. This also shows that in the ensemble formulation the grand-canonical Gibbs state of a finite-size system simulates an infinite system much better than the canonical Gibbs state.

cond-mat.stat-mech↗
arXiv2013

New Formulation of Statistical Mechanics using Thermal Pure Quantum States

We formulate statistical mechanics based on a pure quantum state, which we call a ``thermal pure quantum (TPQ) state''. A single TPQ state gives not only equilibrium values of mechanical variables, such as magnetization and correlation functions, but also those of genuine thermodynamic variables and thermodynamic functions, such as entropy and free energy. Among many possible TPQ states, we discuss the canonical TPQ state, the TPQ state whose temperature is specified. % We also propose there are other TPQ states. In the TPQ formulation of statistical mechanics, thermal fluctuations are completely included in quantum-mechanical fluctuations. As a consequence, TPQ states have much larger quantum entanglement than the equilibrium density operators of the ensemble formulation. We also show that the TPQ formulation is very useful in practical computations, by applying the formulation to a frustrated two-dimensional quantum spin system.

cond-mat.stat-mech↗
arXiv2013

Canonical Thermal Pure Quantum State

A thermal equilibrium state of a quantum many-body system can be represented by a typical pure state, which we call a thermal pure quantum (TPQ) state. We construct the canonical TPQ state, which corresponds to the canonical ensemble of the conventional statistical mechanics. Only a single realization of the TPQ state gives all variables of statistical-mechanical interest. We show that TPQ states corresponding to different ensembles give identical thermodynamic results, and they are related by simple analytic transformations. We have thus completed the TPQ formulation of statistical mechanics. We also show that it has great advantages in practical applications.

cond-mat.stat-mech↗
arXiv2013

Necessity of Superposition of Macroscopically Distinct States for Quantum Computational Speedup

For quantum computation, we investigate the conjecture that the superposition of macroscopically distinct states is necessary for a large quantum speedup. Although this conjecture was supported for a circuit-based quantum computer performing Shor's factoring algorithm [A. Ukena and A. Shimizu, Phys. Rev. A69 (2004) 022301], it needs to be generalized for it to be applicable to a large class of algorithms and/or other models such as measurement-based quantum computers. To treat such general cases, we first generalize the indices for the superposition of macroscopically distinct states. We then generalize the conjecture, using the generalized indices, in such a way that it is unambiguously applicable to general models if a quantum algorithm achieves exponential speedup. On the basis of this generalized conjecture, we further extend the conjecture to Grover's quantum search algorithm, whose speedup is large but quadratic. It is shown that this extended conjecture is also correct. Since Grover's algorithm is a representative algorithm for unstructured problems, the present result further supports the conjecture.

quant-ph↗
arXiv2012

Thermal Pure Quantum States at Finite Temperature

An equilibrium state can be represented by a pure quantum state, which we call a thermal pure quantum (TPQ) state. We propose a new TPQ state and a simple method of obtaining it. A single realization of the TPQ state suffices for calculating all statistical-mechanical properties, including correlation functions and genuine thermodynamic variables, of a quantum system at finite temperature.

cond-mat.stat-mech↗
arXiv2011

General properties of response functions of nonequilibrium steady states

We derive general properties, which hold for both quantum and classical systems, of response functions of nonequilibrium steady states. We clarify differences from those of equilibrium states. In particular, sum rules and asymptotic behaviors are derived, and their implications are discussed. Since almost no assumptions are made, our results are applicable to diverse physical systems. We also demonstrate our results by a molecular dynamics simulation of a many-body interacting system.

cond-mat.stat-mech↗
arXiv2011

Nonequilibrium Molecular Dynamics Simulation of Interacting Many Electrons Scattered by Lattice Vibrations

We propose a new model suitable for a nonequilibrium molecular dynamics (MD) simulation of electrical conductors. The model consists of classical electrons and atoms. The atoms compose a lattice vibration system. The electrons are scattered by electron-electron and electron-atom interactions. Since the scattering cross section is physically more important than the functional form of a scattering potential, we propose to devise the electron-atom interaction potential in such a way that its scattering cross section agrees with that of quantum-mechanical one. To demonstrate advantages of the proposed model, we perform a nonequilibrium MD simulation assuming a doped semiconductor at room or higher temperature. In the linear response regime, we confirm Ohm's law, the dispersion relations and the fluctuation-dissipation relation. Furthermore, we obtain reasonable dependence of the electrical conductivity on temperature, despite the fact that our model is a classical model.

cond-mat.stat-mech↗
arXiv2011

Sum Rules and Asymptotic Behaviors for Optical Conductivity of Nonequilibrium Many-Electron Systems

For many-electron systems, we consider a nonequilibrium state (NES) that is driven by a pump field(s), which is either an optical field or a longitudinal electric field. For the differential optical conductivity describing the differential response of the NES to a probe optical field, we derive exact sum rules and asymptotic behaviors, which open wide possibilities for experiments. In deriving these results, we have also derived universal properties of general differential response functions of time-dependent NESs of general systems.

cond-mat.str-el↗
arXiv2009

Indications of Universal Excess Fluctuations in Nonequilibrium Systems

The fluctuation in electric current in nonequilibrium steady states is investigated by molecular dynamics simulation of macroscopically uniform conductors. At low frequencies, appropriate decomposition of the spectral intensity of current into thermal and excess fluctuations provides a simple picture of excess fluctuations behaving as shot noise. This indicates that the fluctuation-dissipation relation may be violated in a universal manner by the appearance of shot noise for a wide range of systems with particle or momentum transport.

cond-mat.stat-mech↗
arXiv2008

Generalized Phase Rules

For a multi-component system, general formulas are derived for the dimension of a coexisting region in the phase diagram in various state spaces.

cond-mat.stat-mech↗
arXiv2008

Long-time tail in an electric conduction system

The long-time behavior of the velocity autocorrelation function in a classical two-dimensional electric conduction system is studied by the molecular dynamics simulation. In equilibrium, the effect of coexistence of many-body interactions and a random potential is investigated. A crossover from a positive tail proportional to $t^{-1}$, to a negative tail proportional to $-t^{-2}$ is observed as the strength of the random potential increases. In nonequilibrium, the positive tail is enhanced whereas the negative tail appears at earlier times as an electric field increases.

cond-mat.stat-mech↗
arXiv2008

Protected Rabi oscillation induced by natural interactions among physical qubits

For a system composed of nine qubits, we show that natural interactions among the qubits induce the time evolution that can be regarded, at discrete times, as the Rabi oscillation of a logical qubit. Neither fine tuning of the parameters nor switching of the interactions is necessary. Although straightforward application of quantum error correction fails, we propose a protocol by which the logical Rabi oscillation is protected against all single-qubit errors. The present method thus opens a simple and realistic way of protecting the unitary time evolution against noise.

quant-ph↗
arXiv2008

Long-Time Behavior of Velocity Autocorrelation Function for Interacting Particles in a Two-Dimensional Disordered System

The long-time behavior of the velocity autocorrelation function (VACF) is investigated by the molecular dynamics simulation of a two-dimensional system which has both a many-body interaction and a random potential. With strengthening the random potential by increasing the density of impurities, a crossover behavior of the VACF is observed from a positive tail, which is proportional to t^{-1}, to a negative tail, proportional to -t^{-2}. The latter tail exists even when the density of particles is the same order as the density of impurities. The behavior of the VACF in a nonequilibrium steady state is also studied. In the linear response regime the behavior is similar to that in the equilibrium state, whereas it changes drastically in the nonlinear response regime.

cond-mat.stat-mech↗
arXiv2006

Visualization of superposition of macroscopically distinct states

We propose a method of visualizing superpositions of macroscopically distinct states in many-body pure states. We introduce a visualization function, which is a coarse-grained quasi joint probability density for two or more hermitian additive operators. If a state contains superpositions of macroscopically distinct states, one can visualize them by plotting the visualization function for appropriately taken operators. We also explain how to efficiently find appropriate operators for a given state. As examples, we visualize four states containing superpositions of macroscopically distinct states: the ground state of the XY model, that of the Heisenberg antiferromagnet, a state in Shor's factoring algorithm, and a state in Grover's quantum search algorithm. Although the visualization function can take negative values, it becomes non-negative (hence becomes a coarse-grained joint probability density) if the characteristic width of the coarse-graining function used in the visualization function is sufficiently large.

quant-ph↗
arXiv2006

Macroscopic entanglement in Quantum Computation

We investigate macroscopic entanglement of quantum states in quantum computers, where we say a quantum state is entangled macroscopically if the state has superposition of macroscopically distinct states. The index $p$ of the macroscopic entanglement is calculated as a function of the step of the computation, for Grover's quantum search algorithm and Shor's factoring algorithm. It is found that whether macroscopically entangled states are used or not depends on the numbers and properties of the solutions to the problem to be solved. When the solutions are such that the problem becomes hard in the sense that classical algorithms take more than polynomial steps to find a solution, macroscopically entangled states are always used in Grover's algorithm and almost always used in Shor's algorithm. Since they are representative algorithms for unstructured and structured problems, respectively, our results support strongly the conjecture that quantum computers utilize macroscopically entangled states when they solve hard problems much faster than any classical algorithms.

quant-ph↗
arXiv2005

Correlations of observables in chaotic states of macroscopic quantum systems

We study correlations of observables in energy eigenstates of chaotic systems of a large size $N$. We show that the bipartite entanglement of two subsystems is quite strong, whereas macroscopic entanglement of the total system is absent. It is also found that correlations, either quantum or classical, among less than $N/2$ points are quite small. These results imply that chaotic states are stable. Invariance of these properties under local operations is also shown.

quant-ph↗