Langevin dynamics with a tilted periodic potential

We study a Langevin equation for a particle moving in a periodic potential in the presence of viscosity $\gamma$ and subject to a further external field $\alpha$. For a suitable choice of the parameters $\alpha$ and $\gamma$ the related deterministic dynamics yields heteroclinic orbits. In such a regime, in absence of stochastic noise both confined and unbounded orbits coexist. We prove that, with the inclusion of an arbitrarly small noise only the confined orbits survive in a sub-exponential time scale.Comment: 38 pages, 6 figure

The Hydrodynamics of M-Theory

We consider the low energy limit of a stack of N M-branes at finite temperature. In this limit, the M-branes are well described, via the AdS/CFT correspondence, in terms of classical solutions to the eleven dimensional supergravity equations of motion. We calculate Minkowski space two-point functions on these M-branes in the long-distance, low-frequency limit, i.e. the hydrodynamic limit, using the prescription of Son and Starinets [hep-th/0205051]. From these Green's functions for the R-currents and for components of the stress-energy tensor, we extract two kinds of diffusion constant and a viscosity. The N dependence of these physical quantities may help lead to a better understanding of M-branes.Comment: 1+19 pages, references added, section 5 clarified, eq. (72) correcte

Hydrodynamic obstruction to bubble expansion

We discuss a hydrodynamic obstruction to bubble wall acceleration during a cosmological first-order phase transition. The obstruction results from the heating of the plasma in the compression wave in front of the phase transition boundary. We provide a simple criterion for the occurrence of the obstruction at subsonic bubble wall velocity in terms of the critical temperature, the phase transition temperature, and the latent heat of the model under consideration. The criterion serves as a sufficient condition of subsonic bubble wall velocities as required by electroweak baryogenesis.Comment: 18 pages, 4 figures; comments and reference added, published versio

Energy Budget of Cosmological First-order Phase Transitions

The study of the hydrodynamics of bubble growth in first-order phase transitions is very relevant for electroweak baryogenesis, as the baryon asymmetry depends sensitively on the bubble wall velocity, and also for predicting the size of the gravity wave signal resulting from bubble collisions, which depends on both the bubble wall velocity and the plasma fluid velocity. We perform such study in different bubble expansion regimes, namely deflagrations, detonations, hybrids (steady states) and runaway solutions (accelerating wall), without relying on a specific particle physics model. We compute the efficiency of the transfer of vacuum energy to the bubble wall and the plasma in all regimes. We clarify the condition determining the runaway regime and stress that in most models of strong first-order phase transitions this will modify expectations for the gravity wave signal. Indeed, in this case, most of the kinetic energy is concentrated in the wall and almost no turbulent fluid motions are expected since the surrounding fluid is kept mostly at rest.Comment: 36 pages, 14 figure

Coordinate Representation of the One-Spinon One-Holon Wavefunction and Spinon-Holon Interaction

By deriving and studying the coordinate representation for the one-spinon one-holon wavefunction we show that spinons and holons in the supersymmetric $t - J$ model with $1/r^2$ interaction attract each other. The interaction causes a probability enhancement in the one-spinon one-holon wavefunction at short separation between the particles. We express the hole spectral function for a finite lattice in terms of the probability enhancement, given by the one-spinon one-holon wavefunction at zero separation. In the thermodynamic limit, the spinon-holon attraction turns into the square-root divergence in the hole spectral function.Comment: 20 pages, 3 .eps figure

Spontaneous symmetry breaking and the p→0p \to 0 limit

We point out a basic ambiguity in the $p \to 0$ limit of the connected propagator in a spontaneously broken phase. This may represent an indication that the conventional singlet Higgs boson, rather than being a purely massive field, might have a gap-less branch. This would dominate the energy spectrum for ${\bf{p}} \to 0$ and give rise to a very weak, long-range force. The natural interpretation is in terms of density fluctuations of the `Higgs condensate': in the region of very long wavelengths, infinitely larger than the Fermi scale, it cannot be treated as a purely classical c-number field.Comment: 17 pages, LaTex, small changes and some comments adde

Proximity effect in ultrathin Pb/Ag multilayers within the Cooper limit

We report on transport and tunneling measurements performed on ultra-thin Pb/Ag (strong coupled superconductor/normal metal) multilayers evaporated by quench condensation. The critical temperature and energy gap of the heterostructures oscillate with addition of each layer, demonstrating the validity of the Cooper limit model in the case of multilayers. We observe excellent agreement with a simple theory for samples with layer thickness larger than 30\AA . Samples with single layers thinner than 30\AA deviate from the Cooper limit theory. We suggest that this is due to the "inverse proximity effect" where the normal metal electrons improve screening in the superconducting ultrathin layer and thus enhance the critical temperature.Comment: 4 pages, 4 figure

Strong Phase Separation in a Model of Sedimenting Lattices

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a 1-d lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels--- hence the term Strong Phase Separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.Comment: To appear in Phys Rev E (1 January 2000), 16 pages, RevTex, uses epsf, three ps figure

Nonequilibrium thermodynamics versus model grain growth: derivation and some physical implications

Nonequilibrium thermodynamics formalism is proposed to derive the flux of grainy (bubbles-containing) matter, emerging in a nucleation growth process. Some power and non-power limits, due to the applied potential as well as owing to basic correlations in such systems, have been discussed. Some encouragement for such a discussion comes from the fact that the nucleation and growth processes studied, and their kinetics, are frequently reported in literature as self-similar (characteristic of algebraic correlations and laws) both in basic entity (grain; bubble) size as well as time scales.Comment: 8 pages, 1 figur

Phenomenological approach to non-linear Langevin equations

In this paper we address the problem of consistently construct Langevin equations to describe fluctuations in non-linear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property together with the macroscopic knowledge of the system is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time-reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models.Comment: LaTex file, 2 figures available upon request, to appear in Phys.Rev.