Generalized Fokker-Planck equation, Brownian motion, and ergodicity

Microscopic theory of Brownian motion of a particle of mass $M$ in a bath of molecules of mass $m\ll M$ is considered beyond lowest order in the mass ratio $m/M$. The corresponding Langevin equation contains nonlinear corrections to the dissipative force, and the generalized Fokker-Planck equation involves derivatives of order higher than two. These equations are derived from first principles with coefficients expressed in terms of correlation functions of microscopic force on the particle. The coefficients are evaluated explicitly for a generalized Rayleigh model with a finite time of molecule-particle collisions. In the limit of a low-density bath, we recover the results obtained previously for a model with instantaneous binary collisions. In general case, the equations contain additional corrections, quadratic in bath density, originating from a finite collision time. These corrections survive to order $(m/M)^2$ and are found to make the stationary distribution non-Maxwellian. Some relevant numerical simulations are also presented

On the Widder inversion method in problems of statistical mechanics

An alternative way of reconstructing a function from its Laplace transform using the Widder inversion method was shown to be useful in treating some problems of nonequilibrium statistical mechanics. As an example of a successful application of the method, a decay was investigated of the excited atomic state in a simple, but nonetheless physically relevant, model featuring a two-level atom interacting with a continuum of field modes.Показано, що альтернативний спосіб відновлення функції за її образом Лапласа, відомий як метод оберненого перетворення Уіддера, може бути корисним при розв’язуванні деяких проблем нерівноважної статистичної механіки. Як приклад успішного застосування цього підходу розглянуто процес релаксації збудженого стану атома у простій, але фізично змістовній моделі, яка описує взаємодію дворівневого атома з полями в континуальній границі

Transport theory yields renormalization group equations

We show that dissipative transport and renormalization can be described in a single theoretical framework. The appropriate mathematical tool is the Nakajima-Zwanzig projection technique. We illustrate our result in the case of interacting quantum gases, where we use the Nakajima-Zwanzig approach to investigate the renormalization group flow of the effective two-body interaction.Comment: 11 pages REVTeX, twocolumn, no figures; revised version with additional examples, to appear in Phys. Rev.

Several small Josephson junctions in a Resonant Cavity: Deviation from the Dicke Model

We have studied quantum-mechanically a system of several small identical Josephson junctions in a lossless single-mode cavity for different initial states, under conditions such that the system is at resonance. This system is analogous to a collection of identical atoms in a cavity, which is described under appropriate conditions by the Dicke model. We find that our system can be well approximated by a reduced Hamiltonian consisting of two levels per junction. The reduced Hamiltonian is similar to the Dicke Hamiltonian, but contains an additional term resembling a dipole-dipole interaction between the junctions. This extra term arises when states outside the degenerate group are included via degenerate second-order (L\"{o}wdin) perturbation theory. As in the Dicke model, we find that, when N junctions are present in the cavity, the oscillation frequency due to the junction-cavity interaction is enhanced by $\sqrt{N}$. The corresponding decrease in the Rabi oscillation period may cause it to be smaller than the decoherence time due to dissipation, making these oscillations observable. Finally, we find that the frequency enhancement survives even if the junctions differ slightly from one another, as expected in a realistic system.Comment: 11 pages. To be published in Phys. Rev.

Spontaneous emission and lifetime modification caused by an intense electromagnetic field

We study the temporal evolution of a three-level system (such as an atom or a molecule), initially prepared in an excited state, bathed in a laser field tuned at the transition frequency of the other level. The features of the spontaneous emission are investigated and the lifetime of the initial state is evaluated: a Fermi "golden rule" still applies, but the on-shell matrix elements depend on the intensity of the laser field. In general, the lifetime is a decreasing function of the laser intensity. The phenomenon we discuss can be viewed as an "inverse" quantum Zeno effect and can be analyzed in terms of dressed states.Comment: 25 pages, 6 figure

A new perturbative expansion of the time evolution operator associated with a quantum system

A novel expansion of the evolution operator associated with a -- in general, time-dependent -- perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to computational convenience or to satisfy specific requirements. As a remarkable example, the quantum Hamiltonian describing a laser-driven trapped ion is studied in detail.Comment: 32 pages; modified version with examples of my previous paper quant-ph/0404056; to appear on the J. of Optics B: Quantum and Semiclassical Optics, Special Issue on 'Optics and Squeeze Transformations after Einstein

Case Report: Highlighting Male Genital Schistosomiasis (MGS) in Fishermen from the Southwestern Shoreline of Lake Malawi, Mangochi District

Urogenital schistosomiasis causes morbidity within the genitalia but is underreported and infrequently examined in men. To draw attention to male genital schistosomiasis (MGS), a longitudinal cohort study was conducted among fishermen along the southwestern shoreline of Lake Malawi. A case series of five participants is presented inclusive of questionnaire interviews, parasitological examinations, ultrasonography, and provision of a standard dose (40 mg/kg) of praziquantel (PZQ) treatment at baseline, 1-, 3-, 6-, and 12-month follow-up time points. Eggs of Schistosoma haematobium were observed in urine or semen across all time points; parasitological diagnostics were bolstered by real-time PCR for Schistosoma DNA in semen and by portable ultrasonography to document putative MGS-associated morbidity. We highlight the importance of developing standard diagnostic tests for MGS and increasing the accessibility of PZQ treatment to men, especially those in at-risk endemic areas

Resonance fluorescence spectrum in a weak squeezed field with an arbitrary bandwidth

We analyze the linewidth narrowing in the fluorescence spectrum of a two-level atom driven by a squeezed vacuum field of a finite bandwidth. It is found that the fluorescence spectrum in a low-intensity squeezed field can exhibit a (omega - omega(0))(-6) frequency dependence in the wings. We show that this fast fall-off behavior is intimately related to the properties of a narrow-bandwidth squeezed field and does not extend into the region of broadband excitation. We apply the Linear response model and find that the narrowing results from a convolution of the atom response with the spectrum of the incident field. On the experimental side, we emphasize that the linewidth narrowing is not sensitive to the solid angle of the squeezed modes coupled to the atom. We also compare the fluorescence spectrum with the quadrature-noise spectrum and find that the fluorescence spectrum for an off-resonance excitation does not reveal the noise spectrum. We show that this difference arises from the competing three-photon scattering processes. [S1050-2947(98)04308-X]