Density of states of narrow superconducting channels in the regime of quantum fluctuations of the order parameter

The current–voltage characteristics of superconductor–insulator–semiconductor (S1–I–S2) tunnel junctions, where superconducting electrode S2 is a thin nanowire, are studied experimentally. The observed blurring of the gap singularities is interpreted as a manifestation of the order parameter quantum fluctuations. We propose a model taking into account the broadening of the density of states due to the interaction of electrons with the Mooij–Schön plasmon mode emerging in a quasi-one-dimensional superconducting channel in the regime of quantum fluctuations of the order parameter. The model gives results that are in a reasonable qualitative agreement with the experimental data.     

Instability domain of Bose–Einstein condensates with quantum fluctuations and three-body interactions

Through a Gross–Pitaevskii equation comprising cubic, quartic, residual, and quintic nonlinearities, we examine the modulational instability (MI) of Bose–Einstein condensates at higher densities in the presence of quantum fluctuations. We obtain an explicit time-dependent criteria for the MI and the instability domains of the condensates. Solitons are generated by suitably exciting the MI, and their stability is analyzed. We find that quantum fluctuations can completely change the instability of condensates by reversing the nature of the effective two-body interactions. The interplay between three-body interactions and quantum fluctuations is shown. Numerical simulations performed agree with analytical predictions.     

Optimization through quantum annealing: theory and some applications

Quantum annealing is a promising tool for solving optimization problems, similar in some ways to the traditional (classical) simulated annealing of Kirkpatrick et al. Simulated annealing takes advantage of thermal fluctuations in order to explore the optimization landscape of the problem at hand, whereas quantum annealing employs quantum fluctuations. Intriguingly, quantum annealing has been proved to be more effective than its classical counterpart in many applications. We illustrate the theory and the practical implementation of both classical and quantum annealing – highlighting the crucial differences between these two methods – by means of results recently obtained in experiments, in simple toy-models, and more challenging combinatorial optimization problems (namely, Random Ising model and Travelling Salesman Problem). The techniques used to implement quantum and classical annealing are either deterministic evolutions, for the simplest models, or Monte Carlo approaches, for harder optimization tasks. We discuss the pro and cons of these approaches and their possible connections to the landscape of the problem addressed.     

The Influence of Quantum Field Fluctuations on Chaotic Dynamics of Yang–Mills System

Abstract

On example of the model field system we demonstrate that quantum fluctuations of non-abelian gauge fields leading to radiative corrections to Higgs potential and spontaneous symmetry breaking can generate order region in phase space of inherently chaotic classical field system. We demonstrate on the example of another model field system that quantum fluctuations do not influence on the chaotic dynamics of non-abelian Yang–Mills fields if the ratio of bare coupling constants of Yang–Mills and Higgs fields is larger then some critical value. This critical value is estimated.     

Quantum fluctuations in a scale-free network-connected Ising system

We study the effect of quantum fluctuations in an Ising spin system on a scale-free network of degree exponent γ>5 using a quantum Monte Carlo simulation technique. In our model, one can adjust the magnitude of the magnetic field perpendicular to the Ising spin direction and can therefore control the strength of quantum fluctuations for each spin. Our numerical analysis shows that quantum fluctuations reduce the transition temperature T_c of the ferromagnetic-paramagnetic phase transition. However, the phase transition belongs to the same mean-field type universality class both with and without the quantum fluctuations. We also study the role of hubs by turning on the quantum fluctuations exclusively at the nodes with the most links. When only a small number of hub spins fluctuate quantum mechanically, T_c decreases with increasing magnetic field until it saturates at high fields. This effect becomes stronger as the number of hub spins increases. In contrast, quantum fluctuations at the same number of “non-hub” spins do not affect T_c. This implies that the hubs play an important role in maintaining order in the whole network.     

Current characteristics of mesoscopic rings in quantum Smoluchowski regime

In normal mesoscopic metals of a ring topology persistent currents can be induced by threading the center of the ring with a magnetic flux. This phenomenon is an example of the famous Aharonov-Bohm effect. In the paper we study the current vs the external constant magnetic flux characteristics of the system driven by both the classical and the quantum thermal fluctuations. The problem is formulated in terms of Langevin equations in classical and quantum Smoluchowski regimes. We analyze the impact of the quantum thermal fluctuations on the current-flux characteristics. We demonstrate that the current response can be changed from paramagnetic to diamagnetic when the quantum nature of the thermal fluctuations increases.     

Probing the Critical Point of the Jaynes–Cummings Second-Order Dissipative Quantum Phase Transition

We highlight the importance of quantum fluctuations in organizing a dissipative quantum phase transition for the driven Jaynes–Cummings interaction with variable qubit-cavity detuning. The system response presents a substantial difference from the predictions of the semiclassical theory, the extent of which is revealed in the properties of quantum bistability, and visualized with the help of quasi-distribution functions for the cavity field, subject to an appropriate scale parameter. States anticipated by the neoclassical theory of radiation coexist in the quantum picture, following the occurrence of spontaneous dressed-state polarization and phase bistability at resonance.     

Central limit theorem for mixing quantum systems and the CCR-algebra of fluctuations

We analyse macroscopic fluctuations of an infinite quantum system and introduce the CCR-C*-algebra of normal fluctuations. A non-commutative central limit theorem for mixing quantum systems is proved.     

有限温度下一维Gaudin-Yang模型的热力学性质

本文通过数值求解有限温度下一维均匀费米Gaudin-Yang模型的热力学Bethe-ansatz方程, 研究了此模型的基本性质,得到了在给定的温度或给定的相互作用下, 化学势、相互作用、粒子密度和熵的相互变化图像. 对结果分析发现, 在给定温度和相互作用下, 熵随着化学势的变化有一个量子临界区域.     

Emergence of Quantum Mechanics from Theory of Random Fields

Our aim in this paper is to enlighten the possibility to treat quantum mechanics as emergent from a kind of classical physical model, in spite of recent remarkable experiments demonstrating a violation of the Bell inequality. To proceed in a rigorous way, we use the methodology of ontic–epistemic modeling of physical phenomena. This methodology is rooted in the old Bild conception about theoretical and observational models in physics. This conception was elaborated in the fundamental works of Hertz, Boltzmann, and Schrödinger. Our ontic model (generating the quantum model) is of the random field type, prequantum classical statistical field theory (PCSFT). We present a brief review of its basic features without overloading the presentation by mathematical details. Then we show that the Bell inequality can be violated not only at the epistemic level, i.e., for observed correlations, but even at the ontic level, for classical random fields. We devote the important part of the paper to an analysis of the internal energy structure of prequantum random fields and their coupling with the background field of subquantum fluctuations. Finally, we present a unified picture of the microworld based on the composition of prequantum random fields from elementary fluctuations. Since quantum systems are treated as the symbolic representation of prequantum fields, this picture leads to a unifying treatment of all quantum systems as special blocks of elementary fluctuations carrying negligibly small energies.     

Quantum adiabatic transport in the presence of a finite temperature electrodynamic environment

We investigate the influence of electromagnetic fluctuations on quantum transport in a two-dimensional electron gas. We calculate the conductance of a quantum point contact under the influence of transport and gate-voltage fluctuations at finite temperature, using a generalized Landauer-Büttiker approach. The fluctuations are described by a suitable bath of bosons. In contrast to fluctuations of the gate-voltage, transport voltage fluctuations can completely block the electron transport at T = 0. This blockade is lifted as a result of finite temperature of the electrons in the Fermi reservoirs and also of the coupled bosons. In a typical experiment, these two temperatures need not to be the same. We show that the temperature of the coupled bosons limits the accuracy of the conductance quantization of a quantum point contact to a few percent.     

Stability of Semiclassical Gravity Solutions with Respect to Quantum Metric Fluctuations

We discuss the stability of semiclassical gravity solutions with respect to small quantum corrections by considering the quantum fluctuations of the metric perturbations around the semiclassical solution. We call the attention to the role played by the symmetrized 2-point quantum correlation function for the metric perturbations, which can be naturally decomposed into two separate contributions: intrinsic and induced fluctuations. We show that traditional criteria on the stability of semiclassical gravity are incomplete because these criteria based on the linearized semiclassical Einstein equation can only provide information on the expectation value and the intrinsic fluctuations of the metric perturbations. By contrast, the framework of stochastic semiclassical gravity provides a more complete and accurate criterion because it contains information on the induced fluctuations as well. The Einstein–Langevin equation therein contains a stochastic source characterized by the noise kernel (the symmetrized 2-point quantum correlation function of the stress tensor operator) and yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. These points are illustrated with the example of Minkowski space-time as a solution to the semiclassical Einstein equation, which is found to be stable under both intrinsic and induced fluctuations.     

Sensitivity and linearity of superconducting radio-frequency single-electron transistors: effects of quantum charge fluctuations

We have investigated the effects of quantum fluctuations of quasiparticles on the operation of superconducting radio-frequency single-electron transistors (rf-SETs) for large values of the quasiparticle cotunneling parameter alpha = 8EJ/Ec, where EJ and Ec are the Josephson and charging energies. We find that, for alpha > 1, subgap rf-SET operation is still feasible despite quantum fluctuations that wash out quasiparticle tunneling thresholds. Surprisingly, such rf-SETs show linearity and signal-to-noise ratio superior to those obtained when quantum fluctuations are weak, while still demonstrating excellent charge sensitivity.     

Melting of discrete vortices via quantum fluctuations

We consider nonlinear boson states with a nontrivial phase structure in the three-site Bose-Hubbard ring, quantum discrete vortices (or q vortices), and study their "melting" under the action of quantum fluctuations. We calculate the spatial correlations in the ground states to show the superfluid-insulator crossover and analyze the fidelity between the exact and variational ground states to explore the validity of the classical analysis. We examine the phase coherence and the effect of quantum fluctuations on q vortices and reveal that the breakdown of these coherent structures through quantum fluctuations accompanies the superfluid-insulator crossover.     

Quantum fluctuations and magnetic solitons: Equivalence of discrete lattice and renormalized continuum approaches

We discuss quantitative calculations for nonlinear excitations in one-dimensional magnets in the semiclassical regime. We show that the field-theoretic approach—calculating zero point fluctuations in the continuum limit and using counterterms to deal consistently with ultraviolet divergencies—is equivalent to calculating quantum fluctuations for a discrete lattice, if the parameters are identified properly. The latter, technically simpler approach is applied to a calculation of the reduction of soliton induced correlation functions by quantum and thermal fluctuations.Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Role of qubit-cavity entanglement for switching dynamics of quantum interfaces in superconductor metamaterials

We study quantum effects of strong driving field applied to dissipative hybrid qubit-cavity system which are relevant for a realization of quantum gates in superconducting quantum metamaterials. We demonstrate that effects of strong and non-stationary drivings have significantly quantum nature and cannot be treated by means of mean-field approximation. This is shown from a comparison of steady state solution of the standard Maxwell–Bloch equations and numerical solution of Lindblad equation on a density matrix. We show that mean-field approach provides very good agreement with the density matrix solution at not very strong drivings f < f* but at f > f* a growing value of quantum correlations between fluctuations in qubit and photon sectors changes a behavior of the system. We show that in regime of non-adiabatic switching on of the driving such a quantum correlations influence a dynamics of qubit and photons even at weak f.     

Universality of quantum critical dynamics in a planar optical parametric oscillator

We analyze the critical quantum fluctuations in a coherently driven planar optical parametric oscillator. We show that the presence of transverse modes combined with quantum fluctuations changes the behavior of the "quantum image" critical point. This zero-temperature nonequilibrium quantum system has the same universality class as a finite-temperature magnetic Lifshitz transition.     

Near-perfect correlation of the resistance components of mesoscopic samples at the quantum Hall regime

We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the nu=2 and the nu=1 quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall components of the resistance. These correlated fluctuations appear in a magnetic-field range for which the two-terminal resistance of the samples is quantized. We discuss these findings in light of edge-state transport models of the quantum Hall effect. We also show that our results lead to an ambiguity in the determination of the width of quantum Hall transitions.     

Inhomogeneous Modes in the PT-Symmetric Quantum Cosmology

We consider the possibility to solve the issues of the phantom field cosmology by means of the PT-symmetric quantum theory. The Born–Oppenheimer approximation is applied to the Wheeler–DeWitt equation to study the inhomogeneous fluctuations over the homogeneous minisuperspace. The evolution of the longitudinal inhomogeneous modes in WKB-time is described using a time-dependent pseudo-Hermitian effective Hamiltonian.