Quantum annealing by ferromagnetic interaction with the mean-field scheme

Quantum annealing is a novel method for combinatorial optimization problems. In this paper, we discuss the appropriate choice of quantum fluctuations in quantum annealing. The existence of room of choices of quantum fluctuations is an advantage of quantum annealing over simulated annealing. We consider the ferromagnetic interaction as a source of quantum fluctuations. Using the mean-field annealing scheme, we show that quantum annealing by ferromagnetic interaction is more efficient than the conventional quantum annealing and simulated annealing in the ground state search of the random-field Ising model.     

Quantum polarization spectroscopy of ultracold spinor gases

We propose a method for the detection of ground state quantum phases of spinor gases through a series of two quantum nondemolition measurements performed by sending off-resonant, polarized light pulses through the gas. Signatures of various mean-field as well as strongly correlated phases of F=1 and F=2 spinor gases obtained by detecting quantum fluctuations and mean values of polarization of transmitted light are identified.     

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.     

Quantum decoherence of the damped harmonic oscillator

In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations. The text was submitted by the author in English.     

Quantum correction to conductivity close to a ferromagnetic quantum critical point in two dimensions

We study the temperature dependence of the conductivity due to quantum interference processes for a two-dimensional disordered itinerant electron system close to a ferromagnetic quantum critical point. Near the quantum critical point, the crossover between diffusive and ballistic regimes of quantum interference effects occurs at a temperature T*=1/taugamma(E(F)tau)2, where gamma is the parameter associated with the Landau damping of the spin fluctuations, tau is the impurity scattering time, and E(F) is the Fermi energy. For a generic choice of parameters, T* is smaller than the nominal crossover scale 1/tau. In the ballistic quantum critical regime, the conductivity behaves as T1/3.     

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.     

Quantum decoherence and classical correlations of the harmonic oscillator in the Lindblad theory

In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. The transition from quantum to classical behaviour of the considered system is analysed and it is shown that the classicality takes place during a finite interval of time. We calculate also the decoherence time and show that it has the same scale as the time after which statistical fluctuations become comparable with quantum fluctuations.     

Squeezing States of Magnons in a Ferromagnet

In this paper, we conduct an investigation into magnon self-squeezing states in a ferromagnet. In these states, the quantum fluctuations of the spin components can be lower than the zero-point quantum fluctuations of the coherent states. Through calculating the expectation values of spin fluctuations we gain the condition of achieving magnon self-squeezing. We introduce the mean-field theory for dealing with the nonlinear interaction term of Hamiltonian of magnon system.     

Quantum-phase transition in a XY model

In this paper we study quantum-phase transition in the one-dimensional XY model with an XY easy-plane single ion anisotropy. We use the path-integral formalism, but consider the effect of quantum fluctuations, which renormalize the parameters of the system, using the self-consistent harmonic approximation. We show that the quantum fluctuations increase the effective coupling constant of the model.     

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.     

Constraints on operator ordering from third quantization

In this paper, we analyse the Wheeler–DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes classical at later stages during the cosmic expansion. This is physically expected, if the universe is formed from quantum fluctuations in the third quantized formalism. So, we will argue that this physical requirement can be used to constrain the form of the operator ordering chosen. We will explicitly demonstrate this to be the case for two different cosmological models.     

Quantum Gravity,Information Theory and the CMB

We review connections between the metric of spacetime and the quantum fluctuations of fields. We start with the finding that the spacetime metric can be expressed entirely in terms of the 2-point correlator of the fluctuations of quantum fields. We then discuss the open question whether the knowledge of only the spectra of the quantum fluctuations of fields also suffices to determine the spacetime metric. This question is of interest because spectra are geometric invariants and their quantization would, therefore, have the benefit of not requiring the modding out of diffeomorphisms. Further, we discuss the fact that spacetime at the Planck scale need not necessarily be either discrete or continuous. Instead, results from information theory show that spacetime may be simultaneously discrete and continuous in the same way that information can. Finally, we review the recent finding that a covariant natural ultraviolet cutoff at the Planck scale implies a signature in the cosmic microwave background (CMB) that may become observable.     

Fluctuations and Correlations of Pure Quantum Turbulence in Superfluid 3He-B

We describe the first measurements of line-density fluctuations and spatial correlations of quantum turbulence in superfluid 3He-B. All of the measurements are performed in the low-temperature regime, where the normal-fluid density is negligible. The quantum turbulence is generated by a vibrating grid. The vortex-line density is found to have large length-scale correlations, indicating large-scale collective motion of vortices. Furthermore, we find that the power spectrum of fluctuations versus frequency obeys a -5/3 power law which verifies recent speculations that this behavior is a generic feature of fully developed quantum turbulence, reminiscent of the Kolmogorov spectrum for velocity fluctuations in classical turbulence.     

Fluctuations of an Evaporating Black Hole from Back Reaction of Its Hawking Radiation: Questioning a Premise in Earlier Work

This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum fields in an evaporating black hole. We explain how the stochastic gravity formalism can be a useful tool for that purpose within a low-energy effective field theory approach to quantum gravity. As an explicit example we apply it to the study of the spherically-symmetric sector of metric perturbations around an evaporating black hole background geometry. For macroscopic black holes we find that those fluctuations grow and eventually become important when considering sufficiently long periods of time (of the order of the evaporation time), but well before the Planckian regime is reached. In addition, the assumption of a simple correlation between the fluctuations of the energy flux crossing the horizon and far from it, which was made in earlier work on spherically-symmetric induced fluctuations, is carefully analyzed and found to be invalid. Our analysis suggests the existence of an infinite amplitude for the fluctuations of the horizon as a three-dimensional hypersurface. We emphasize the need for understanding and designing operational ways of probing quantum metric fluctuations near the horizon and extracting physically meaningful information. Dedicated to Rafael Sorkin on the occasion of his 60th birthday.     

Nonequilibrium dynamics of the Bose-Hubbard model: a projection-operator approach

We study the phase diagram and nonequilibrium dynamics involving ramp of the hopping amplitude J(t)=Jt/τ with ramp time τ of the Bose-Hubbard model at zero temperature using a projection-operator formalism which allows us to incorporate the effects of quantum fluctuations beyond mean-field approximations in the strong-coupling regime. Our formalism yields a phase diagram which provides a near exact match with quantum Monte Carlo results in three dimensions. We also compute the residual energy Q, the superfluid order parameter Δ(t), the equal-time order parameter correlation function C(t), and the wave function overlap F which yields the defect formation probability P during nonequilibrium dynamics of the model. We find that Q, F, and P do not exhibit the expected universal scaling. We explain this absence of universality and show that our results compare well with recent experiments.     

Work and work fluctuations in quantum systems

With the development of quantum thermodynamics [1], it turned out that the existence of a thermal equilibrium can be derived directly from quantum mechanics. This finding has raised the question, what other thermodynamic concepts could be applied to quantum systems and how they might emerge from quantum mechanics. Here, we discuss how the concept of work translates to quantum systems and how its emergence can be understood. Moreover, we show that even for small and simple quantum systems, work may be a meaningful concept. We then address the question of work fluctuations in quantum systems. We discuss the Jarzynski relation and its quantum counterparts and we show that corresponding relations hold even for open quantum systems.     

Will Small Particles Exhibit Brownian Motion in the Quantum Vacuum?

The Brownian motion of small particles interacting with a field at a finite temperature is a well-known and well-understood phenomenon. At zero temperature, even though the thermal fluctuations are absent, quantum fields still possess vacuum fluctuations. It is then interesting to ask whether a small particle that is interacting with a quantum field will exhibit Brownian motion when the quantum field is assumed to be in the vacuum state. In this paper, we study the cases of a small charge and an imperfect mirror interacting with a quantum scalar field in (1 + 1) dimensions. Treating the quantum field as a classical stochastic variable, we write down a Langevin equation for the particles. We show that the results we obtain from such an approach agree with the results obtained from the fluctuation-dissipation theorem. Unlike the finite temperature case, there exists no special frame of reference at zero temperature and hence it is essential that the particles do not break Lorentz invariance. We find that that the scalar charge breaks Lorentz invariance, whereas the imperfect mirror does not. We conclude that small particles such as the imperfect mirror will exhibit Brownian motion even in the quantum vacuum, but this effect can be so small that it may prove to be difficult to observe it experimentally.     

Scalar field fluctuations in the early universe

We compute the quantum fluctuations of a non-self-interacting but unstable scalar field of arbitrary mass during the period of inflation. Instead of treating the scalar field in a static De Sitter space, we begin with a scalar field in the Friedmann universe just before the start of inflation, and work out the dynamics of the growing quantum fluctuation of the field after it has entered into the inflationary epoch. We use the physically sensible method of Vilenkin to regularize the theory. We find that in all but two special cases the fluctuations produced are different from those in a static De Sitter space, and the effect of the finite width of the scalar field limits the growth of fluctuations.