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.     

Macroscopic quantum tunneling in d-wave YBa2Cu3O7-delta Josephson junctions

The escape rate from the zero voltage state in a superconducting Josephson junction (JJ) is determined by the temperature, but it saturates at low temperature due to macroscopic quantum tunneling (MQT). Complications due to d-wave symmetry in a high temperature superconductor, like low energy quasiparticles and an unconventional current-phase relation, may influence the escape rate. We report, for the first time to our knowledge, the observation of MQT in a YBa(2)Cu(3)O(7-delta) grain boundary biepitaxial JJ. This proves that dissipation can be significantly reduced by a proper junction configuration, which is of significance for quantum coherence.     

Investigation of Noise-Induced Escape Rate: A Quantum Mechanical Approach

A quantum system coupled to a heat-bath in non-equilibrium environment is considered to study the problem of noise-induced escape rate from a metastable state in the moderate to strong friction limit (Kramers’ regime). It is known that starting from an initial coherent state representation of bath oscillators, one can derive a c-number generalized quantum Langevin equation where the quantum correction terms appear as a coupled infinite set of hierarchy of equations. For practical purpose, one should truncate these equations after a certain order. In our present development, we calculate the quantum correction terms in a closed analytical form based on a systematic perturbation technique and then derive the lowest order quantum correction factor exactly in the case of an Ohmic dissipative bath. Finally, to demonstrate its applicability, the effective equation of motions has been used to study the barrier crossing dynamics which incorporates the quantum correction factors.     

Fokker–Planck Equations as Scaling Limits of Reversible Quantum Systems

We consider a quantum particle moving in a harmonic exterior potential and linearly coupled to a heat bath of quantum oscillators. Caldeira and Leggett derived the Fokker–Planck equation with friction for the Wigner distribution of the particle in the large-temperature limit; however, their (nonrigorous) derivation was not free of criticism, especially since the limiting equation is not of Lindblad form. In this paper we recover the correct form of their result in a rigorous way. We also point out that the source of the diffusion is physically restrictive under this scaling. We investigate the model at a fixed temperature and in the large-time limit, where the origin of the diffusion is a cumulative effect of many resonant collisions. We obtain a heat equation with a friction term for the radial process in phase space and we prove the Einstein relation in this case.     

Thermal dissipation in quantum turbulence

The microscopic mechanism of thermal dissipation in quantum turbulence is numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipation works at large scales and it affects the vortex dynamics. We successfully obtain the mutual friction coefficients of the vortex in dilute Bose-Einstein condensates dynamics as functions of temperature.     

The dynamical-quantization approach to open quantum systems

The dynamical-quantization approach to open quantum systems does consist in quantizing the Brownian motion starting directly from its stochastic dynamics under the framework of both Langevin and Fokker–Planck equations, without alluding to any model Hamiltonian. On the ground of this non-Hamiltonian quantization method, we can derive a non-Markovian Caldeira–Leggett quantum master equation as well as a non-Markovian quantum Smoluchowski equation. The former is solved for the case of a quantum Brownian particle in a gravitational field whilst the latter for a harmonic oscillator. In both physical situations, we come up with the existence of a non-equilibrium thermal quantum force and investigate its classical limit at high temperatures as well as its quantum limit at zero temperature. Further, as a physical application of our quantum Smoluchowski equation, we take up the tunneling phenomenon of a non-inertial quantum Brownian particle over a potential barrier. Lastly, we wish to point out, corroborating conclusions reached in our previous paper [A. O. Bolivar, Ann. Phys. 326 (2011) 1354], that the theoretical predictions in the present article uphold the view that our non-Hamiltonian quantum mechanics is able to capture novel features inherent in quantum Brownian motion, thereby overcoming shortcomings underlying the Caldeira–Leggett Hamiltonian model.     

Brownian motion of a classical particle in quantum environment

The Klein–Kramers equation, governing the Brownian motion of a classical particle in a quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.     

Evidence of two-dimensional macroscopic quantum tunneling of a current-biased dc SQUID

The escape probability out of the superconducting state of a hysteretic dc SQUID has been measured at different values of the applied magnetic flux. At low temperatures, the escape current and the width of the probability distribution are temperature independent but they depend on flux. Experimental results do not fit the usual one-dimensional macroscopic quantum tunneling (MQT) law but are perfectly accounted for by the two-dimensional MQT behavior as we propose here. Near zero flux, our data confirms the recent MQT observation in a dc SQUID [Phys. Rev. Lett. 89, 98301 (2002)]].     

Escape of stars from gravitational clusters in the Chandrasekhar model

We study the evaporation of stars from globular clusters using the simplified Chandrasekhar model [S. Chandrasekhar, Dynamical friction. II. The rate of escape of stars from clusters and the evidence for the operation of dynamical friction, Astrophys. J. 97 (1943) 263]. This is an analytically tractable model giving reasonable agreement with more sophisticated models that require complicated numerical integrations. In the Chandrasekhar model: (i) the stellar system is assumed to be infinite and homogeneous (ii) the evolution of the velocity distribution of stars f(v,t) is governed by a Fokker-Planck equation, the so-called Kramers-Chandrasekhar equation (iii) the velocities |v| that are above a threshold value R>0 (escape velocity) are not counted in the statistical distribution of the system. In fact, high velocity stars leave the system, due to free evaporation or to the attraction of a neighboring galaxy (tidal effects). Accordingly, the total mass and energy of the system decrease in time. If the star dynamics is described by the Kramers-Chandrasekhar equation, the mass decreases to zero exponentially rapidly. Our goal is to obtain non-perturbative analytical results that complement the seminal studies of Chandrasekhar, Michie and King valid for large times t→+∞ and large escape velocities R→+∞. In particular, we obtain an exact semi-explicit solution of the Kramers-Chandrasekhar equation with the absorbing boundary condition f(R,t)=0. We use it to obtain an explicit expression of the mass loss at any time t when R→+∞. We also derive an exact integral equation giving the exponential evaporation rate λ(R), and the corresponding eigenfunction f_λ(v), when t→+∞ for any sufficiently large value of the escape velocity R. For R→+∞, we obtain an explicit expression of the evaporation rate that refines the Chandrasekhar results. More generally, our results can have applications in other contexts where the Kramers equation applies, like the classical diffusion of particles over a barrier of potential (Kramers problem).     

Friction and diffusion coefficients in coordinate in nonequilibrium nuclear processes

The influence of different sets of friction and diffusion coefficients on the dynamics of a nuclear system is investigated. Taking as an example a dinuclear system we show in a “classic” investigation that with zero diffusion in the coordinate, the uncertainty relation can be violated during short initial times. Sets of diffusion coefficients are found for which the “classic” and quantum diffusion equations give close physical results. The tunneling through an energy barrier is sensitively influenced by the friction and diffusion coefficients in coordinate in the diffusion equation.     

Density quantization of metallic hydrogen

A cellular model of atomic hydrogen is hypothesized in which the Fermi pressure due to a single foreign electron invading the cell is examined in lieu of the entire degenerate gas. The Schrödinger equation is then solved in a self-consistent fashion with Laplace's equation for the electronic cloud. The Wronskian of the two possible wave functions does not vanish because the homogeneous Neumann condition is applied to the surface of the cell, while the Coulomb singularity compels a solution to be generated from the origin. Two quantum numbers result, one for the energy and one for the density, thus there is a lower limit to the density at zero temperature. Further corrections for electron waves by the Born Von-Karmen conditions broadens the radial quantum number into a continuum, but with an absolute lower limit to the density given by the ground state solutions to the Schrödinger equation.We obtain a bulk modulus of compressibility for metallic hydrogen of about 4.66×10¹² dynes/g on the average over a pressure range of 1 to 25 megabars with a density range of 0.4 to 4 g/cc. This is about a factor of 2 greater than Wigner and Huntington's estimate (1935). The zero temperature pressure and density at a maximum is 20.05 Mb and 4.8 g/cc. At the density Wigner and Huntington propose (0.8 g/cc) for the metallic modification, we obtain a necessary pressure of 2.2 Mb. Wigner and Huntington suggest 0.25 Mb while Stewart's data (1956) suggest about 1 Mb. Recent investigations in the literature run the gamut from 1 to 20 Mb (Alder & Christian, 1960). Furthermore, we obtain a latent heat of fusion of 134.3 kcal/g at maximum density, which decreases to zero at 19.1 Mb. The result means that the metallic state of hydrogen exists only over a pressure range of 1 Mb and below 19 Mb, it is a viscoelastic fluid until the molecular solid, formed above 20 Mb begins to form a plasma.     

Temperature Dependence of Photoluminescence from Single and Ensemble InAs/GaAs Quantum Dots

We investigate the temperature dependence of photoluminescence from single and ensemble InAs/GaAs quantum dots systematically. As temperature increases, the exciton emission peak for single quantum dot shows broadening and redshift. For ensemble quantum dots, however, the exciton emission peak shows narrowing and fast redshift. We use a simple steady-state rate equation model to simulate the experimental data of photoluminescence spectra. It is confirmed that carrier-phonon scattering gives the broadening of the exciton emission peak in single quantum dots while the effects of carrier thermal escape and retrapping play an important role in the narrowing and fast redshift of the exciton emission peak in ensemble quantum dots.     

Microscopic derivation of quantum fluctuations in nuclear reactions

The coupling between collective and intrinsic states of a nucleus is treated with first order time-dependent perturbation theory at zero temperature. In addition to the friction constant and conservative potential corrections, general expressions for the diffusion constants and differential equations in time for the second moments are derived for position and momentum dependent couplings, and are calculated in a particular solvable model. As a result, the diffusion constants do not necessarily vanish at zero temperature but there remain pure quantum effects. For oscillatory collective motion, the low temperature limit of the Einstein relation is given and an existence theorem for damped pure quantum states is derived.     

Interaction quench in the Hubbard model

Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the opposite limit of Landau's Fermi-liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is, the interaction is switched on at time t=0. Using the flow equation method, we are able to study the real time dynamics for weak interaction U in a systematic expansion and find three clearly separated time regimes: (i) An initial buildup of correlations where the quasiparticles are formed. (ii) An intermediate quasi-steady regime resembling a zero temperature Fermi liquid with a nonequilibrium quasiparticle distribution function. (iii) The long-time limit described by a quantum Boltzmann equation leading to thermalization of the momentum distribution function with a temperature T proportional, variantU.     

Topological order at nonzero temperature

We propose a definition for topological order at nonzero temperature in analogy to the usual zero temperature definition that a state is topologically ordered, or "nontrivial", if it cannot be transformed into a product state (or a state close to a product state) using a local (or approximately local) quantum circuit. We prove that any two-dimensional Hamiltonian which is a sum of commuting local terms is not topologically ordered at T > 0. We show that such trivial states cannot be used to store quantum information using certain stringlike operators. This definition is not too restrictive, however, as the four dimensional toric code does have a nontrivial phase at nonzero temperature.     

The Investigation of Gauge Transformations in the SLq(2) Gauge Field and Thermodynamics Model

Some problems about global transformations in the SLq(2) gauge field and correlative thermodynamics model have been investigated in this paper. We proved that the quantum trace of gauge potential is not gauge-invariant if we compose two GLq(2) gauge transformations. In addition, it has been discovered in SLq(2) thermodynamics model that thermodynamics average of an observable quantity does not satisfy similar gauge invariance. We also found that the thermodynamics average can be only calculated in the case of zero energy gap. This fact shows that the q-deformed energy equation in superconductivity theory is unable to derive naturally from quantum trace model.     

Two-species fermion mixtures with population imbalance

We analyze the phase diagram of uniform superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BEC) limit as a function of the scattering parameter and population imbalance. We find at zero temperature that the phase diagram of population imbalance versus scattering parameter is asymmetric for unequal masses, having a larger stability region for uniform superfluidity when the lighter fermions are in excess. In addition, we find topological quantum phase transitions associated with the disappearance or appearance of momentum space regions of zero quasiparticle energies. Lastly, near the critical temperature, we derive the Ginzburg-Landau equation and show that it describes a dilute mixture of composite bosons and unpaired fermions in the BEC limit.     

Quantum Discord of Two Atoms Interacting with a Single-mode Thermal Field

This paper investigates the quantum discord and entanglement of two atoms when they simultaneously interact with a single-mode thermal field. The results show that, the two atoms which are initially in separate states can be entangled by a thermal field. However, with increase of the mean photon number, the value of the entanglement decreases and disappears when the temperature of the cavity is high enough (corresponding to the large value of the mean photon number). In stark contrast, the quantum discord does not decrease, but gradually reaches stable value at high temperature. In addition, when the two atoms are initially the Werner mixed state, we have found that, a large amount of quantum discord is exist even in the region where the entanglement is zero, which is a strong signature for the presence of non classical correlations. These results indicate that, the quantum discord is more resistant to the environment’s disturbance than the entanglement for higher temperatures.     

Quantum Entanglement and Correlation Lengths of a S-wave Superconductors in the Presence of a Weak Constant External Potential

By considering a s-wave Bardeen-Cooper-Schrieffer superconductor, as a many body system, subject to a weak constant external potential, U, using perturbed linearized Gorkov equations at zero temperature and calculating perturbed Green’s functions up to the first approximation, we obtain the two-particle space-spin density matrix of the system. Then, we investigate the effect of the potential on bipartite entanglement (via concurrence) of electron spins of a Cooper pair and also quantum discord in terms of the potential and the relative distance of electrons of a Cooper pair, r. At some fixed values of r, concurrence is zero and does not change until U increases and receives to a special value. Specially, quantum entanglement length and quantum correlation length (in which quantum discord becomes zero) with respect to the potential are derived. We result that by increasing the potential, these lengths are increased. At higher values of U, quantum correlation length is not very sensitive to changes in U. Finally, the relation between these lengths is given.