arXiv subjects

Ilki Kim

Publications and source records attributed to Ilki Kim.

At least 19 recordsLinked to original sources

arXiv2026

Spectral Softening and the Structural Breakdown of Thermodynamic Equilibrium

Under sufficiently slow driving, thermodynamics predicts reversible evolution through a sequence of equilibrium states. We show that this expectation fails near spectral degeneracy in driven quadratic Hamiltonian systems. As the soft-mode frequency collapses, the intrinsic dynamical timescale diverges and quadratic confinement is lost, leading to a breakdown of timescale separation and the failure of adiabatic following even under arbitrarily slow driving. More precisely, adiabaticity is lost once the soft-mode frequency falls below a finite, drive-dependent threshold, implying that the breakdown extends over a finite regime rather than being confined to a singular limit. Crucially, this dynamical instability is accompanied by a divergence of the canonical partition function, rendering equilibrium ensembles ill-defined and eliminating the foundation of quasistatic thermodynamic processes. This breakdown does not arise from unbounded Hamiltonians or critical slowing down, but emerges structurally from spectral softening within a bounded quadratic system. Analysis of the Wigner phase-space representation, together with its classical counterpart, reveals the same singular structure, demonstrating that this limitation is not uniquely quantum but originates from the underlying Hamiltonian phase-space geometry. These results show that thermodynamic reversibility is fundamentally constrained, as a direct consequence of the breakdown of equilibrium, whenever spectral softening removes an intrinsic frequency scale.

cond-mat.stat-mech↗

arXiv2020

Quantal-classical fluctuation relation and the second law of thermodynamics: The quantum linear oscillator

In this work, we study the fluctuation relation and the second law of thermodynamics within a quantum linear oscillator externally driven over the period of time t = tau. To go beyond the standard approach (the two-point projective measurement one) to this subject and also render it discussed in both quantum and classical domains on the single footing, we recast this standard approach in terms of the Wigner function and its propagator in the phase space (x,p). With the help of the canonical transformation from (x,p) to the angle-action coordinates (ϕ,I), we can then derive a measurement-free (classical-like) form of the Crooks fluctuation relation in the Wigner representation. This enables us to introduce the work W_{I_0,I_{tau}} associated with a single run from (I_0) to (I_{tau}) over the period tau, which is a quantum generalization of the thermodynamic work with its roots in the classical thermodynamics. This quantum work differs from the energy difference e_{I_0,I_{tau}} = e(I_{tau}) - e(I_0) unless beta, hbar --> 0. Consequently, we will obtain the quantum second-law inequality Delta F_{beta} \leq _{P} \leq _{P} = Delta U, where P, Delta F_{beta}, and _P denote the work (quasi)-probability distribution, the free energy difference, and the average work distinguished from the internal energy difference Delta U, respectively, while _P --> Delta U in the limit of beta, hbar --> 0 only. Therefore, we can also introduce the quantum heat Q_q = Delta U - W even for a thermally isolated system, resulting from the quantum fluctuation therein. This is a more fine-grained result than _P = Delta U obtained from the standard approach. Owing to the measurement-free nature of the thermodynamic work W_{I_0,I_{tau}}, our result can also apply to the (non-thermal) initial states rho_0 = (1-gamma) rho_{beta} + gamma sigma with sigma \ne rho_{beta}.

cond-mat.stat-mech↗

arXiv2019

Non-negative Wigner-like distributions and Renyi-Wigner entropies of arbitrary non-Gaussian quantum states: The thermal state of the one-dimensional box problem

In this work, we consider the phase-space picture of quantum mechanics. We then introduce non-negative Wigner-like (operational) distributions \widetilde{\mathcal W}_{rho;alpha}(x,p) corresponding to the density operator \hat{rho} and being proportional to {W_{rho^(alpha/2)}(x,p)}^2, where W_{rho}(x,p) denotes the usual Wigner function. In doing so, we utilize the formal symmetry between the purity measure Tr(rho^2) and its Wigner representation (2 pi hbar) \int dx dp {W_{rho}(x,p)}^2 and then consider, as a generalization, such symmetry between the fractional moment Tr(\hat{rho}^{alpha}) and its Wigner representation (2 pi hbar) \int dx dp {W_{rho^{alpha/2}}(x,p)}^2. Next, we create a framework that enables explicit evaluation of the Renyi-Wigner entropies for the classical-like distributions \widetilde{\mathcal W}_{rho;alpha}(x,p). Consequently, a better understanding of some non-Gaussian features of a given state rho will be given, by comparison with the Gaussian state rho_G defined in terms of its Wigner function W_{rho_G}(x,p) and essentially determined by its purity measure T(rho_G)^2 alone. To illustrate the validity of our framework, we evaluate the distributions \widetilde{\mathcal W}_{beta;alpha}(x,p) corresponding to the (non-Gaussian) thermal state rho_β of a single particle confined by a one-dimensional infinite potential well with either the Dirichlet or Neumann boundary condition and then analyze the resulting Renyi entropies. Our phase-space approach will also contribute to a deeper understanding of non-Gaussian states and their properties either in the semiclassical limit (hbar \to 0) or in the high-temperature limit (beta \to 0), as well as enabling us to systematically discuss the quantal-classical Second Law of Thermodynamics on the single footing.

cond-mat.stat-mech↗

arXiv2018

Renyi-alpha entropies of quantum states in closed form: Gaussian states and a class of non-Gaussian states

In this work, we study the Renyi-alpha entropies S_{alpha}(\hat{rho}) = (1 - alpha)^{-1} \ln{Tr(\hat{rho}^{alpha})} of quantum states for N bosons in the phase-space representation. With the help of the Bopp rule, we derive the entropies of Gaussian states in closed form for positive integers alpha = 2,3,4, ... and then, with the help of the analytic continuation, acquire the closed form also for real values of alpha > 0. The quantity S_2(\hat{rho}), primarily studied in the literature, will then be a special case of our finding. Subsequently we acquire the Renyi-alpha entropies, with positive integers alpha, in closed form also for a specific class of the non-Gaussian states (mixed states) for N bosons, which may be regarded as a generalization of the eigenstates |n> (pure states) of a single harmonic oscillator with n >= 1, in which the Wigner functions have negative values indeed. Due to the fact that the dynamics of a system consisting of $N$ oscillators is Gaussian, our result will contribute to a systematic study of the Renyi-alpha entropy dynamics when the current form of a non-Gaussian state is initially prepared.

cond-mat.stat-mech↗

arXiv2017

Endo-reversible heat engines coupled to finite thermal reservoirs: A rigorous treatment

We consider two specific thermodynamic cycles of engine operating in a finite time coupled to two thermal reservoirs with a finite heat capacity: The Carnot-type cycle and the Lorenz-type cycle. By means of the endo-reversible thermodynamics, we then discuss the power output of engine and its optimization. In doing so, we treat the temporal duration of a single cycle rigorously, i.e., without neglecting the duration of its adiabatic parts. Then we find that the maximally obtainable power output P_m and the engine efficiency η_m at the point of P_m explicitly depend on the heat conductance and the compression ratio. From this, it is immediate to observe that the well-known results available in many references, in particular the (compression-ratio-independent) Curzon-Ahlborn-Novikov expressions such as η_m --> η_{CAN} = 1 - (T_L/T_H)^(1/2) with the temperatures (T_H, T_L) of hot and cold reservoirs only, can be recovered, but, significantly enough, in the limit of a vanishingly small heat conductance and an infinitely large compression ratio only. Our result implies that the endo-reversible model of a thermal machine operating in a finite time and so producing a finite power output with the Curzon-Ahlborn-Novikov results should be limited in its own validity regime.

physics.gen-ph↗

arXiv2017

Heat Engines running upon a Non-Ideal Fluid Model with Higher Efficiencies than upon the Ideal Gas Model

We consider both Otto and Diesel heat engine cycles running upon the working substances modeled by the van der Waals fluid as a simple non-ideal gas model. We extensively perform the efficiency study in these model engines. Then we find that this "real" engine model can go beyond its ideal-gas counterpart in efficiency, whereas as well-known, the maximum Carnot efficiency is the same for both ideal and non-ideal gas engines. In fact, the higher the density of non-ideality is, the higher efficiency tends to be found, especially in the low-temperature regime, but with more shrinkage in the range of physically allowed compression ratio, determined by the Carnot upper bound, namely, the Second Law of thermodynamics. Our findings imply that in addition to the engine architectures and bath temperatures, the properties of working substances should also be taken into consideration in the performance study of heat engines, the theoretical model aspects of which have not sufficiently been discussed so far. It is straightforward that our methodology may also apply for other non-ideal fluid models.

cond-mat.stat-mech↗

arXiv2014

Heat transport through a quantum Brownian harmonic chain beyond the weak-coupling regime: An exact treatment

We consider a linear chain of quantum harmonic oscillators, in which the number of the individual oscillators is given by an arbitrary number N, and each oscillator is coupled at an arbitrary strength kappa to its nearest neighbors ("intra-coupling"), as well as the two end oscillators of the chain are coupled at an arbitrary strength c_nu to two separate baths at arbitrarily different temperatures, respectively. We derive an exact closed expression for the steady-state heat current flowing from a hot bath through the chain to a cold bath, in the Drude-Ullersma damping model going beyond the Markovian damping. This allows us to explore the behavior of heat current relative to the intra-coupling strength as a control parameter, especially in pursuit of the heat power amplification. Then it turns out that in the weak-coupling regime (kappa, c_nu << 1), the heat current is small, as expected, and almost independent of chain length N, hence violating Fourier's law of heat conduction; this is consistent to the earlier results obtained within the rotating wave approximation for the intra-coupling as well as in the Born-Markov approximation for the chain-bath coupling. Beyond the weak-coupling regime, on the other hand, we typically observe that with increase of the intra-coupling strength the heat current is gradually amplified, and reaches its maximum value at some specific coupling strength kappa_R "resonant" to a given chain-bath coupling strength. Also, the behavior of heat current versus chain length appears typically in such a way that the magnitude of current reaches its maximum with N=1 and then gradually decreases with increase of the chain length, being in fact almost N-independent in the range of N large enough. As a result, Fourier's law proves violated also in this regime.

cond-mat.stat-mech↗

arXiv2014

Jarzynski equality and the second law of thermodynamics beyond the weak-coupling limit: The quantum Brownian oscillator

We consider a time-dependent quantum linear oscillator coupled to a bath at an arbitrary strength. We then introduce a generalized Jarzynski equality (GJE) which includes the terms reflecting the system-bath coupling. This enables us to study systematically the coupling effect on the linear oscillator in a non-equilibrium process. This is also associated with the second law of thermodynamics beyond the weak-coupling limit. We next take into consideration the GJE in the classical limit. By this generalization we show that the Jarzynski equality in its original form can be associated with the second law, in both quantal and classical domains, only in the vanishingly small coupling regime.

cond-mat.stat-mech↗

arXiv2012

Electrostatic-field-induced dynamics in an ultrathin quantum well

We consider the time evolution of a particle subjected to both a uniform electrostatic field F and a one-dimensional delta-function potential well. We derive the propagator K_F(x,t|x',0) of this system, directly leading to the wavefunction psi_F(x,t), in which its essential ingredient K_F(0,t|0,0), accounting for the ionization-recombination in the bound-continuum transition, is exactly expressed in terms of the multiple hypergeometric functions F(z_1,z_2,...,z_n). And then we obtain the ingredient K_F(0,t|0,0) in an appropriate approximation scheme, expressed in terms of the generalized hypergeometric functions p_F_q(z) being much more transparent to physically interpret and much more accessible in their numerical evaluation than the functions F(z_1,z_2,...,z_n).

quant-ph↗

arXiv2011

Non-equilibrium dynamics in the quantum Brownian oscillator and the second law of thermodynamics

We initially prepare a quantum linear oscillator weakly coupled to a bath in equilibrium at an arbitrary temperature. We disturb this system by varying a Hamiltonian parameter of the coupled oscillator, namely, either its spring constant or mass according to an arbitrary but pre-determined protocol in order to perform external work on it. We then derive a closed expression for the reduced density operator of the coupled oscillator along this non-equilibrium process as well as the exact expression pertaining to the corresponding quasi-static process. This immediately allows us to analytically discuss the second law of thermodynamics for non-equilibrium processes. Then we derive a Clausius inequality and obtain its validity supporting the second law, as a consistent generalization of the Clausius equality valid for the quasi-static counterpart, introduced in [1].

cond-mat.stat-mech↗

arXiv2010

Field-induced dynamics in the quantum Brownian oscillator: An exact treatment

We consider a quantum linear oscillator coupled to a bath in equilibrium at an arbitrary temperature and then exposed to an external field arbitrary in form and strength. We then derive the reduced density operator in closed form of the coupled oscillator in a non-equilibrium state at an arbitrary time.

cond-mat.stat-mech↗

arXiv2007

The second law of thermodynamics in the quantum Brownian oscillator at an arbitrary temperature

In the classical limit no work is needed to couple a system to a bath with sufficiently weak coupling strength (or with arbitrarily finite coupling strength for a linear system) at the same temperature. In the quantum domain this may be expected to change due to system-bath entanglement. Here we show analytically that the work needed to couple a single linear oscillator with finite strength to a bath cannot be less than the work obtainable from the oscillator when it decouples from the bath. Therefore, the quantum second law holds for an arbitrary temperature. This is a generalization of the previous results for zero temperature [1,2]; in the high temperature limit we recover the classical behavior.

quant-ph↗

arXiv2007

An analytic study of the ionization from an ultrathin quantum well in a weak electrostatic field

We consider the time evolution of a particle bound by an attractive one-dimensional delta-function potential (at x = 0) when a uniform electrostatic field (F) is applied. We explore explicit expressions for the time-dependent wavefunction ψ_F(x,t) and the ionization probability {\mathcal{P}}(t), respectively, in the weak-field limit. In doing so, ψ_F(0,t) is a key element to their evaluation. We obtain a closed expression for ψ_F(0,t) which is an excellent approximation of the exact result being a numerical solution of the Lippmann-Schwinger integral equation. The resulting probability density |ψ_F(0,t)|^2, as a simple alternative to {\mathcal{P}}(t), is also in good agreement to its counterpart from the exact one. In doing this, we also find a new and useful integral identity of the Airy function.

quant-ph↗

arXiv2007

Comment on "note on the derivative of the hyperbolic cotangent"

In a couple of articles (Ford G W and O'Connell R F 1996 Nature 380 113 and 2002 J. Phys. A: Math. Gen. 35 4183) it was argued that the standard result for the derivative of the hyperbolic cotangent in the literature, d \coth y/dy = -{csch}^2 y is incomplete and the correct expression should have an additional term proportional to the Dirac delta function. The purpose of this paper is to demonstrate that this claim is incorrect.

quant-ph↗

arXiv2002

Computational leakage: Grover's algorithm with imperfections

We study the effects of dissipation or leakage on the time evolution of Grover's algorithm for a quantum computer. We introduce an effective two-level model with dissipation and randomness (imperfections), which is based upon the idea that ideal Grover's algorithm operates in a 2-dimensional Hilbert space. The simulation results of this model and Grover's algorithm with imperfections are compared, and it is found that they are in good agreement for appropriately tuned parameters. It turns out that the main features of Grover's algorithm with imperfections can be understood in terms of two basic mechanisms, namely, a diffusion of probability density into the full Hilbert space and a stochastic rotation within the original 2-dimensional Hilbert space.

quant-ph↗

arXiv2001

Delayed-choice measurement and temporal nonlocality

We study for a composite quantum system with a quantum Turing architecture the temporal non-locality of quantum mechanics by using the temporal Bell inequality, which will be derived for a discretized network dynamics by identifying the subsystem indices with (discrete) parameter time. However, the direct ``observation'' of the quantum system will lead to no violation of the temporal Bell inequality and to consistent histories of any subsystem. Its violation can be demonstrated, though, for a delayed-choice measurement.

quant-ph↗

arXiv2000

Uncertainty rescued: Bohr's complementarity for composite systems

Generalized uncertainty relations may depend not only on the commutator relation of two observables considered, but also on mutual correlations, in particular, on entanglement. The equivalence between the uncertainty relation and Bohr's complementarity thus holds in a much broader sense than anticipated.

quant-ph↗

arXiv2000

Quantum network architecture of tight-binding models with substitution sequences

We study a two-spin quantum Turing architecture, in which discrete local rotations α_m of the Turing head spin alternate with quantum controlled NOT-operations. Substitution sequences are known to underlie aperiodic structures. We show that parameter inputs α_m described by such sequences can lead here to a quantum dynamics, intermediate between the regular and the chaotic variant. Exponential parameter sensitivity characterizing chaotic quantum Turing machines turns out to be an adequate criterion for induced quantum chaos in a quantum network.

quant-ph↗