Ayumu Sugita

Second moment of the Husimi distribution as a measure of complexity of quantum states.

We propose the second moment of the Husimi distribution as a measure of complexity of quantum states. The inverse of this quantity represents the effective volume in phase space occupied by the Husimi distribution, and has a good correspondence with chaoticity of classical system. Its properties are similar to the classical entropy proposed by Wehrl, but it is much easier to calculate numerically. We calculate this quantity in the quartic oscillator model, and show that it works well as a measure of chaoticity of quantum states.

Geometrical pumping in quantum transport: Quantum master equation approach

For an open quantum system, we investigate the pumped current induced by a slow modulation of control parameters on the basis of the quantum master equation and full counting statistics. We find that the average and the cumulant generating function of the pumped quantity are characterized by the geometrical Berry-phase-like quantities in the parameter space, which is associated with the generator of the master equation. From our formulation, we can discuss the geometrical pumping under the control of the chemical potentials and temperatures of reservoirs. We demonstrate the formulation by spinless electrons in coupled quantum dots. We show that the geometrical pumping is prohibited for the case of non-interacting electrons if we modulate only temperatures and chemical potentials of reservoirs, while the geometrical pumping occurs in the presence of an interaction between electrons.

Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems

For open systems described by the quantum Markovian master equation, we study a possible extension of the Clausius equality to quasistatic operations between nonequilibrium steady states (NESSs). We investigate the excess heat divided by temperature (i.e., excess entropy production) which is transferred into the system during the operations. We derive a geometrical expression for the excess entropy production, which is analogous to the Berry phase in unitary evolution. Our result implies that in general one cannot define a scalar potential whose difference coincides with the excess entropy production in a thermodynamic process, and that a vector potential plays a crucial role in the thermodynamics for NESSs. In the weakly nonequilibrium regime, we show that the geometrical expression reduces to the extended Clausius equality derived by Saito and Tasaki (J. Stat. Phys. 145:1275, 2011). As an example, we investigate a spinless electron system in quantum dots. We find that one can define a scalar potential when the parameters of only one of the reservoirs are modified in a non-interacting system, but this is no longer the case for an interacting system.

Proof of the generalized Lieb-Wehrl conjecture for integer indices larger than one

Gnutzmann and Życzkowski have proposed the Renyi–Wehrl entropy as a generalization of the Wehrl entropy, and conjectured that its minimum is obtained for coherent states. We prove this conjecture for the Renyi index q = 2, 3, ... in the cases of compact semisimple Lie groups. A general formula for the minimum value is given.

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 fewer 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.

Typical Pure States and Nonequilibrium Processes in Quantum Many-Body Systems

We show that it is possible to calculate equilibrium expectation values of many-body correlated quantities such as the characteristic functions and probability distributions with the use of only a single typical pure state. It also means that we can apply the pure state approach to Heisenberg operators and their spectral fluctuation, and hence to nonequilibrium processes starting from equilibrium. In particular, we can accurately analyze the full statistics of entropy production in nonequilibrium mesoscopic systems. In this way, we can access the full information on higher-order fluctuations in the large deviation regime far from equilibrium.

The fall of the black hole firewall: natural nonmaximal entanglement for the Page curve

The black hole firewall conjecture is based on Page curve hypothesis, which claims that entanglement between black hole and Hawking radiation is almost maximum. The hypothesis is inspired by Lubkin-Lloyd-Pagels-Page theorem for degenerate systems with zero Hamiltonian. Adopting canonical typicality for nondegenerate systems with nonvanishing Hamiltonians, the entanglement becomes nonmaximal,and energetic singularities (firewalls) do not emerge for general systems. For static thermal pure states of black hole and Hawking radiation, entanglement entropy equals thermal entropy of the smaller system.

A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

We develop a method of calculating the nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system using a Redfield-type quantum master equation (QME). We decompose the Redfield QME into a Lindblad-type QME and the remaining part

Diffusion in the Markovian limit of the spatio-temporal colored noise

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The effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems

. Regarding the steady state of the Lindblad QME as the unperturbed solution, we perform a perturbative calculation with respect to