A combinatorial formula for homogeneous moments

We establish a combinatorial formula for homogeneous moments and give some examples where it can be put to use. An application to the statistical mechanics of interacting gauged vortices is discussed.Comment: 8 pages, LaTe

O(N) symmetry-breaking quantum quench: Topological defects versus quasiparticles

We present an analytical derivation of the winding number counting topological defects created by an O(N) symmetry-breaking quantum quench in N spatial dimensions. Our approach is universal in the sense that we do not employ any approximations apart from the large-$N$ limit. The final result is nonperturbative in N, i.e., it cannot be obtained by %the usual an expansion in 1/N, and we obtain far less topological defects than quasiparticle excitations, in sharp distinction to previous, low-dimensional investigations.Comment: 6 pages of RevTex4-1, 1 figure; to be published in Physical Review

On A New Class of Tempered Stable Distributions: Moments and Regular Variation

We extend the class of tempered stable distributions first introduced in Rosinski 2007. Our new class allows for more structure and more variety of tail behaviors. We discuss various subclasses and the relation between them. To characterize the possible tails we give detailed results about finiteness of various moments. We also give necessary and sufficient conditions for the tails to be regularly varying. This last part allows us to characterize the domain of attraction to which a particular tempered stable distribution belongs

Quarkonium states in a complex-valued potential

We calculate quarkonium binding energies using a realistic complex-valued potential for both an isotropic and anisotropic quark-gluon plasma. We determine the disassociation temperatures of the ground and first excited states considering both the real and imaginary parts of the binding energy. We show that the effect of momentum-space anisotropy is smaller on the imaginary part of the binding energy than on the real part of the binding energy. In the case that one assumes an isotropic plasma, we find disassociation temperatures for the J/psi, Upsilon and chi_b of 1.6 T_c, 2.8 T_c, and 1.5 T_c, respectively. We find that a finite oblate momentum-space anisotropy increases the disassociation temperature for all states considered and results in a splitting of the p-wave states associated with the chi_b first excited state of bottomonium.Comment: 23 pages, 9 figures; v4: subtraction of V_infinity corrected to only subtract Re[V_infinity

Single-file dynamics with different diffusion constants

We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF. For the general N-particle case (N large) we perform stochastic simulations using our new computationally efficient stochastic simulation technique based on the Gillespie algorithm. We find that the mean square displacement for a tagged particle scales as the square root of time (as for identical particles) for long times, with a prefactor which depends on the diffusion constants for the particles; these results are in excellent agreement with very recent analytic predictions in the mathematics literature.Comment: 9 pages, 5 figures. Journal of Chemical Physics (in press

Acoustic Kappa-Density Fluctuation Waves in Suprathermal Kappa Function Fluids

We describe a new wave mode similar to the acoustic wave in which both density and velocity fluctuate. Unlike the acoustic wave in which the underlying distribution is Maxwellian, this new wave mode occurs when the underlying distribution is a suprathermal kappa function and involves fluctuations in the power law index, kappa. This wave mode always propagates faster than the acoustic wave with an equivalent effective temperature and becomes the acoustic wave in the Maxwellian limit as kappa goes to infinity.Comment: 11 pages, 2 figures, in press AS

Inelastic effects in molecular junctions in the Coulomb and Kondo regimes: Nonequilibrium equation-of-motion approach

Inelastic effects in the Coulomb blockade and Kondo regimes of electron transport through molecular junctions are considered within a simple nonequilibrium equation-of-motion (EOM) approach. The scheme is self-consistent, and can qualitatively reproduce the main experimental observations of vibrational features in Coulomb blockade [H.Park et al., Nature 407, 57 (2000)] and Kondo [L.H.Yu et al., Phys. Rev. Lett. 93, 266802 (2004)] regimes. Considerations similar to the equilibrium EOM approach by Meir et al. [Phys. Rev. Lett. 66, 3048 (1991); ibid. 70, 2601 (1993)] are used on the Keldysh contour to account for the nonequilibrium nature of the junction, and dressing by appropriate Franck-Condon (FC) factors is used to account for vibrational features. Results of the equilibrium EOM scheme by Meir et al. are reproduced in the appropriate limit.Comment: 12 pages, 5 figure

Minimal length scales for the existence of local temperature

We review a recent approach to determine the minimal spatial length scales on which local temperature exists. After mentioning an experiment where such considerations are of relevance, we first discuss the precise definition of the existence of local temperature and its physical relevance. The approach to calculate the length scales in question considers homogenous chains of particles with nearest neighbor interactions. The entire chain is assumed to be in a thermal equilibrium state and it is analyzed when such an equilibrium state at the same time exists for a local part of it. The result yields estimates for real materials, the liability of which is discussed in the sequel. We finally consider a possibility to detect the existence or non-existence of a local thermal state in experiment.Comment: review, 13 pages, 11 figure

Large fluctuations in stochastic population dynamics: momentum space calculations

Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the probability distribution of the population size is transformed into an evolution equation for the probability generating function. Spectral decomposition then brings about an eigenvalue problem for a non-Hermitian linear differential operator. The ground-state eigenmode encodes the stationary distribution of the population size. For long-lived metastable populations which exhibit extinction or escape to another metastable state, the quasi-stationary distribution and the mean time to extinction or escape are encoded by the eigenmode and eigenvalue of the lowest excited state. If the average population size in the stationary or quasi-stationary state is large, the corresponding eigenvalue problem can be solved via WKB approximation amended by other asymptotic methods. We illustrate these ideas in several model examples.Comment: 20 pages, 9 figures, to appear in JSTA

Rigorous Born Approximation and beyond for the Spin-Boson Model

Within the lowest-order Born approximation, we present an exact calculation of the time dynamics of the spin-boson model in the ohmic regime. We observe non-Markovian effects at zero temperature that scale with the system-bath coupling strength and cause qualitative changes in the evolution of coherence at intermediate times of order of the oscillation period. These changes could significantly affect the performance of these systems as qubits. In the biased case, we find a prompt loss of coherence at these intermediate times, whose decay rate is set by $\sqrt{\alpha}$, where $\alpha$ is the coupling strength to the environment. We also explore the calculation of the next order Born approximation: we show that, at the expense of very large computational complexity, interesting physical quantities can be rigorously computed at fourth order using computer algebra, presented completely in an accompanying Mathematica file. We compute the $O(\alpha)$ corrections to the long time behavior of the system density matrix; the result is identical to the reduced density matrix of the equilibrium state to the same order in $\alpha$. All these calculations indicate precision experimental tests that could confirm or refute the validity of the spin-boson model in a variety of systems.Comment: Greatly extended version of short paper cond-mat/0304118. Accompanying Mathematica notebook fop5.nb, available in Source, is an essential part of this work; it gives full details of the fourth-order Born calculation summarized in the text. fop5.nb is prepared in arXiv style (available from Wolfram Research