arXiv subjects

Tomio Petrosky

Publications and source records attributed to Tomio Petrosky.

At least 19 recordsLinked to original sources

arXiv2025

Energy-Efficient Pseudo-Ratchet for Brownian Computers through One-Dimensional Quantum Brownian Motion

Brownian computers utilize thermal fluctuations as a resource for computation and hold promise for achieving ultra-low-energy computations. However, the lack of a statistical direction in Brownian motion necessitates the incorporation of ratchets that facilitate the speeding up and completion of computations in Brownian computers. To make the ratchet mechanism work effectively, an external field is required to overcome thermal fluctuations, which has the drawback of increasing energy consumption. As a remedy for this drawback, we introduce a new approach based on one-dimensional (1D) quantum Brownian motion, which exhibits intrinsic unidirectional transport even in the absence of external forces or asymmetric potential gradients, thereby functioning as an effective pseudo-ratchet. Specifically, we exploit that quantum resonance effects in 1D systems divide the momentum space of particles into subspaces. These subspaces have no momentum inversion symmetry, resulting in the natural emergence of unidirectional flow. We analyze this pseudo-ratchet mechanism without energy dissipation from an entropic perspective and show that it remains consistent with the second law of thermodynamics.

cond-mat.stat-mech↗

arXiv2025

Analytical Treatment of a Non-integrable Pendulum Based on Eigenvalue Problem of the Liouville Operator

We perform analytical and quantitative analysis of the motion of a non-integrable pendulum with two degrees of freedom, in which an integrable nonlinear pendulum and a harmonic oscillator are weakly coupled through a non-integrable perturbative interaction, based on the eigenvalue problem of the Liouvillian that is the generator of time evolution in classical mechanics. The eigenfunctions belonging to the zero eigenvalue of the Liouvillian correspond to the invariants of the motion. The zero eigenvalue of the integrable unperturbed Liouvillian is infinitely degenerate at the resonance point. By applying a perturbation, level repulsion occurs between the eigenstates of the unperturbed system, and some of the degeneracy is lifted, resulting in a non-zero eigenvalue. In order to evaluate the frequency gap caused by the level repulsion, we introduce an auxiliary operator called the collision operator which is well known in non-equilibrium statistical mechanics. We show that the dependence of the magnitude of frequency gap on the coupling constant can be quantitatively evaluated by simply finding the condition for the existence of the collision operator, without directly solving the eigenvalue problem.

nlin.CD↗

arXiv2024

Stability of Hilda asteroids at 3:2 resonance point in restricted three-body problem

Stability of Hilda Asteroids in the solar system around the 3:2 resonance point is analyzed in terms of the Sun-Jupiter-asteroid elliptic restricted three-body problem. We show that the Hamiltonian of the system is well-approximated by a single-resonance Hamiltonian around the 3:2 resonance. This implies that orbits of the Hilda asteroids are approximately integrable, thus their motion is stable. This is in contrast to other resonances such as the 3:1 and the 2:1 resonances at which Kirkwood gaps occur. Indeed, around the 3:1 and the 2:1 resonances, the Hamiltonians are approximated by double-resonance Hamiltonians that are nonintegrable and thus indicate chaotic motions. By a suitable canonical transformation, we reduce the number of degrees of freedom for the system and derive a Hamiltonian which has two degrees of freedom. As a result, we can analyze the stability of the motion by constructing Poincare surface of section.

astro-ph.EP↗

arXiv2024

Enhanced classical radiation damping of electronic cyclotron motion in the vicinity of the Van Hove singularity in a waveguide

We study the damping process of electron cyclotron motion and the resulting emission in a waveguide using the classical Friedrichs model without relying on perturbation analysis such as Fermi's golden rule. A classical Van Hove singularity appears at the lower bound (or cut-off frequency) of the dispersion associated with each of the electromagnetic field modes in the waveguide. In the vicinity of the Van Hove singularity, we found that not only is the decay process associated with the resonance pole enhanced (amplification factor ~ $10^4$) but the branch-point effect is also comparably enhanced. As a result, the timescale on which most of the decay occurs is dramatically shortened. Further, this suggests that the non-Markovian branch point effect should be experimentally observable in the vicinity of the Van Hove singularity. Our treatment yields a physically-acceptable solution without the problematic runaway solution that is well known to appear in the traditional treatment of classical radiation damping based on the Abraham-Lorentz equation.

physics.class-ph↗

arXiv2020

Anomalous diffusion in Davydov quantum molecular chain model

We discuss anomalous relaxation processes in Davydov one-dimensional chain molecule that consists of an exciton and an acoustic phonon field as a thermal reservoir in the chain. We derive a kinetic equation for the exciton using the complex spectral representation of the Liouville-von Neumann operator. Due to the one-dimensionality, the momentum space separates into infinite sets of disjoint irreducible subspaces dynamically independent of one another. Hence, momentum relaxation occurs only within each subspace toward the Maxwell distribution. We obtain a hydrodynamic mode with transport coefficients, a sound velocity and a diffusion coefficient, defined in each subspace. Moreover, because the sound velocity has momentum dependence, phase mixing affects the broadening of the spatial distribution of the exciton in addition to the diffusion process. Due to the phase mixing the increase rate of the mean-square displacement of the exciton increases linearly with time and diverges in the long-time limit.

cond-mat.stat-mech↗

arXiv2018

Dynamics of high-harmonic generation in terms of complex Floquet spectral analysis

High-harmonic generation (HHG) of a two-level-system driven by an intense monochromatic phase-locked laser is studied in terms of complex spectral analysis with the Floquet method. In contrast to the phenomenological approaches, this analysis deals with the whole process as a coherent quantum process based on microscopic dynamics. The spectral decomposition corresponding to the contributions of the Floquet resonance and dressed continuous states of the total system have been obtained. The calculated HHG spectrum exhibits the characteristic features of the HHG from solids. We found that the quantum interference of the Floquet resonance states is responsible for the transition from the adiabatic to the stationary regime in the HHG process and that the phase of the driving laser controls the dynamics of the HHG photon emission.

quant-ph↗

arXiv2017

Analysis of high-harmonic generation in terms of complex Floquet spectral analysis

Recent developments on intense laser sources is opening a new field of optical sciences. An intense coherent light beam strongly interacting with the matter causes a coherent motion of a particle, forming a strongly dressed excited particle. A photon emission from this dressed excited particle is a strong nonlinear process causing high-harmonic generation(HHG), where the perturbation analysis is broken down. In this work, we study a coherent photon emission from a strongly dressed excited atom in terms of complex spectral analysis in the extended Floquet-Hilbert-space. We have obtained the eigenstates of the total Hamiltonian with use of Feshbach-Brilloiun-Wigner projection method. In this extended space, the eigenstates of the total Hamiltonian consisting of the radiation field and the atom system have complex eigenvalues whose imaginary part represents the decay rate. Time evolution of the system is represented by the complex eigenvector expansion so that the correlation dynamics between the photon and the atom is fully taken into account. The HHG is interpreted as the irreversible spontaneous photon emission due to the resonance singularity in terms of the multiple Floquet states that are generated by periodic external field. We have found that the interference between the emitted photons over the different Floquet states causes spatial pulse emission correlated with the decay process of the excited atom.

quant-ph↗

arXiv2017

Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics

At the exceptional point where two eigenstates coalesce in open quantum systems, the usual diagonalization scheme breaks down and the Hamiltonian can only be reduced to Jordan block form. Most of the studies on the exceptional point appearing in the literature introduce a phenomenological effective Hamiltonian that essentially reduces the problem to that of a finite non-Hermitian matrix for which it is straightforward to obtain the Jordan form. In this paper, we demonstrate how the Hamiltonian of an open quantum system reduces to Jordan block form at an exceptional point in an exact manner that treats the continuum without any approximation. Our method relies on the Brillouin-Wigner-Feshbach projection method according to which we can obtain a finite dimensional effective Hamiltonian that shares the discrete sector of the spectrum with the original Hamiltonian. While owing to its eigenvalue dependence this effective Hamiltonian cannot be used to write the Jordan block directly, we show that by formally extending the problem to include eigenstates with complex eigenvalues that reside outside the usual Hilbert space, we can obtain the Jordan block form at the exceptional point without introducing any approximation. We also introduce an extended Jordan form basis away from the exceptional point, which provides an alternative way to obtain the Jordan block at an exceptional point. The extended Jordan block connects continuously to the Jordan block exactly at the exceptional point implying that the observable quantities are continuous at the exceptional point.

quant-ph↗

arXiv2016

Higher-order Time-Symmetry-Breaking Phase Transition due to meeting of an Exceptional Point and Fano Resonance

We have theoretically investigated the time-symmetry breaking phase transition process for two discrete states coupled with a one-dimensional continuum by solving the nonlinear eigenvalue prob- lem for the effective Hamiltonian associated with the discrete spectrum. We obtain the effective Hamiltonian with use of the Feshbach-Brillouin-Wigner projection method. Strong energy depen- dence of the self-energy appearing in the effective Hamiltonian plays a key role in the time-symmetry breaking phase transition: as a result of competition in the decay process between the Van Hove singularity and the Fano resonance, the phase transition becomes a higher-order transition when both the two discrete states are located near the continuum threshold.

quant-ph↗

arXiv2015

Microscopic Description of Quantum Lorentz Gas by Complex Spectral Representation of the Liouville-von Neumann Equation: A Limitation of the Boltzmann Approximation

Irreversible processes of one-dimensional quantum perfect Lorentz gas is studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouville-von Neumann operator. A limitation of the usual phenomenological Boltzmann equation is discussed from this dynamical point of view. For a Wigner distribution function that spreads over moderately small scale comparative to the mean-free-path, we found a shifting motion in space of the distribution that cannot be described by the hydrodynamic approximation of the kinetic equation. The mechanism of the shifting has two completely different origins: one is due to different value of the imaginary part of the eigenvalue of the Liouvillian and predominates in moderately small wavenumber associated to the spatial distribution, while the other is due to the existence of the real part of the eigenvalue associated to a wave propagation and predominates in moderately large wavenumber.

cond-mat.stat-mech↗

arXiv2014

Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas

We propose a non-singular representation for a non-Hermitian operator even if the parameter space contains exceptional points (EPs), at which the operator cannot be diagonalized and the usual spectral representation ceases to exist. Our representation has a generalized Jordan block form and is written in terms of extended pseudo-eigenstates. Our method is free from a divergence in the spectral representation at EPs, at which multiple eigenvalues and eigenvectors coalesce and the eigenvectors cannot be normalized. Our representation improves the accuracy of numerical calculations of physical quantities near EPs. We also find that our method is applicable to various problems related to EPs in the parameter space of non-Hermitian operators. We demonstrate the usefulness of our representation by investigating Boltzmann's collision operator in a one-dimensional quantum Lorentz gas in the weak coupling approximation.

cond-mat.stat-mech↗

arXiv2014

Enhanced resonant force between two entangled identical atoms in a photonic crystal

We consider the resonant interaction energy and force between two identical atoms, one in an excited state and the other in the ground state, placed inside a photonic crystal. The atoms, having the same orientation of their dipole moment, are supposed prepared in their symmetrical state and interact with the quantum electromagnetic field. We consider two specific models of photonic crystals: a one-dimensional model and an isotropic model. We show that in both cases the resonant interatomic force can be strongly enhanced by the presence of the photonic crystal, as a consequence of the modified dispersion relation and density of states, in particular if the transition frequency of the atoms is close to the edge of a photonic gap. Differences between the two models considered of photonic crystal are discussed in detail, as well as comparison with the analogous system of two impurity atoms in a quantum semiconductor wire. A numerical estimate of the effect in a realistic situation is also discussed.

quant-ph↗

arXiv2013

Tunable Bound States in Continuum by Optical Frequency

We demonstrate the existence of tunable bound-states in continuum (BIC) in a 1-dimensional quantum wire with two impurities induced by an intense monochromatic radiation field. We found that there is a new type of BIC due to the Fano interference between two optical transition channels, in addition to the ordinary BIC due to a geometrical interference between electron wave functions emitted by impurities. In both cases the BIC can be achieved by tuning the frequency of the radiation field.

quant-ph↗

arXiv2012

Amplification of non-Markovian decay due to bound state absorption into continuum

It is known that quantum systems yield non-exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time `near zone' and long time `far zone.' In the near zone the survival probability falls off according to a $t^{-1}$ power law, and in the far zone it falls off as $t^{-3}$. We show that the timescale $T_Q$ separating these two regions is inversely related to the gap between the discrete bound state energy and the continuum threshold. In the case that the bound state is absorbed into the continuum and vanishes, then the time scale $T_Q$ diverges and the survival probability follows the $t^{-1}$ power law even on asymptotic scales. Conversely, one could study the case of an anti-bound state approaching the threshold before being ejected from the continuum to form a bound state. Again the $t^{-1}$ power law dominates precisely at the point of ejection.

quant-ph↗

arXiv2011

Band Structure and Accumulation Point in the Spectrum of Quantum Collision Operator in a One-Dimensional Molecular Chain

We consider the eigenvalue problem of a kinetic collision operator for a quantum Brownian particle interacting with a one-dimensional chain. The quantum nature of the system gives rise to a difference operator. For the one-dimensional case, the momentum space separates into infinite sets of disjoint subspaces dynamically independent of one another. The eigenvalue problem of the collision operator is solved with the continued fraction method. The spectrum is non-negative, possesses an accumulation point and exhibits a band structure. We also construct the eigenvectors of the collision operator and establish their completeness and orthogonality relations in each momentum subspaces.

cond-mat.stat-mech↗

arXiv2010

Nonequilibrium Transport of Quantum Molecular Chain in terms of the Complex Liouvillian Spectrum

Transport process in molecular chain in nonequilibrium stationary state is theoretically investigated. The molecule is interacting at its both ends with thermal baths which has different temperatures, while no dissipation mechanism is contained inside the molecular chain. We have first obtained the nonequilibrium stationary state outside the Hilbert space in terms of the complex spectral representation of Liouvillian. The nonequilibrium stationary state is obtained as an eigenstate of the Liouvillian which is constructed through the collision invariant of the kinetic equation. The eigenstate of the Liouvillian contains an information of spatial correlation between the molecular chain and the thermal baths. While energy flow in the nonequilibrium state which is due to the first order correlation can be described by Landauer formula, the particle current due to the second order correlation cannot be described by the Landauer formula. The present method provides a simple and perspective way to evaluate the energy transport of molecular chain under the nonequilibrium situation.

cond-mat.stat-mech↗

arXiv2010

Nontrivial eigenvalues of the Liouvillian of an open quantum system

We present methods of finding complex eigenvalues of the Liouvillian of an open quantum system. The goal is to find eigenvalues that cannot be predicted from the eigenvalues of the corresponding Hamiltonian. Our model is a T-type quantum dot with an infinitely long lead. We suggest the existence of the non-trivial eigenvalues of the Liouvillian in two ways: one way is to show that the original problem reduces to the problem of a two-particle Hamiltonian with a two-body interaction and the other way is to show that diagram expansion of the Green's function has correlation between the bra state and the ket state. We also introduce the integral equations equivalent to the original eigenvalue problem.

cond-mat.stat-mech↗

arXiv2007

Quasi-bound states in continuum

We report the prediction of quasi-bound states (resonant states with very long lifetimes) that occur in the eigenvalue continuum of propagating states for a wide region of parameter space. These quasi-bound states are generated in a quantum wire with two channels and an adatom, when the energy bands of the two channels overlap. A would-be bound state that lays just below the upper energy band is slightly destabilized by the lower energy band and thereby becomes a resonant state with a very long lifetime (a second QBIC lays above the lower energy band).

quant-ph↗