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arXiv2000

Inertial effects in three dimensional spinodal decomposition of a symmetric binary fluid mixture: A lattice Boltzmann study

The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamicaly consistent lattice Boltzmann method. We combine results from simulations with different numerical parameters to obtain an unprecendented range of length and time scales when expressed in reduced physical units. Using eight large (256^3) runs, the resulting composite graph of reduced domain size l against reduced time t covers 1 < l < 10^5, 10 < t < 10^8. Our data is consistent with the dynamical scaling hypothesis, that l(t) is a universal scaling curve. We give the first detailed statistical analysis of fluid motion, rather than just domain evolution, in simulations of this kind, and introduce scaling plots for several quantities derived from the fluid velocity and velocity gradient fields.

cond-mat↗

arXiv2001

Magnetic Susceptibility of the Balian-Werthamer Phase of 3He in Aerogel

The equilibrium superfluid phase of 3He impregnated into high-porosity silica aerogels appears to be a non-equal-spin-pairing state in zero field at all pressures, which is generally assumed to be the Balian-Werthamer (BW) phase modified by the depairing effects of the aerogel structure. The nuclear magnetic susceptibility played a key role in identifying the B-phase of pure 3He with the BW state. We report theoretical calculations of the nuclear magnetic susceptibility for the BW model of superfluid 3He in aerogel within the framework of the Fermi-liquid theory of superfluid 3He. Scattering of quasiparticles by the aerogel, in addition to Fermi-liquid exchange corrections, leads to substantial changes in the susceptibility of the BW phase. The increase in the magnetic susceptibility of 3He-aerogel compared to pure 3He-B is related to the polarizability of the gapless excitations and the impurity-induced local field. The limited data that is available is in rough agreement with theoretical predictions. Future measurements could prove important for a more definitive identification of the ordered phase, as well as for refining the theoretical model for the effects of disorder and scattering on the properties of superfluid 3He.

cond-mat↗

arXiv2002

Interacting Bosons at Finite Temperature: How Bogolubov Visited a Black Hole and Came Home Again

The structure of the thermal equilibrium state of a weakly interacting Bose gas is of current interest. We calculate the density matrix of that state in two ways. The most effective method, in terms of yielding a simple, explicit answer, is to construct a generating function within the traditional framework of quantum statistical mechanics. The alternative method, arguably more interesting, is to construct the thermal state as a vector state in an artificial system with twice as many degrees of freedom. It is well known that this construction has an actual physical realization in the quantum thermodynamics of black holes, where the added degrees of freedom correspond to the second sheet of the Kruskal manifold and the thermal vector state is a state of the Unruh or the Hartle-Hawking type. What is unusual about the present work is that the Bogolubov transformation used to construct the thermal state combines in a rather symmetrical way with Bogolubov's original transformation of the same form, used to implement the interaction of the nonideal gas in linear approximation. In addition to providing a density matrix, the method makes it possible to calculate efficiently certain expectation values directly in terms of the thermal vector state of the doubled system.

gr-qc↗

arXiv1997

Slow modes in passive advection

The anomalous scaling in the Kraichnan model of advection of the passive scalar by a random velocity field with non-smooth spatial behavior is traced down to the presence of slow resonance-type collective modes of the stochastic evolution of fluid trajectories. We show that the slow modes are organized into infinite multiplets of descendants of the primary conserved modes. Their presence is linked to the non-deterministic behavior of the Lagrangian trajectories at high Reynolds numbers caused by the sensitive dependence on initial conditions within the viscous range where the velocity fields are more regular. Revisiting the Kraichnan model with smooth velocities we describe the explicit solution for the stationary state of the scalar. The properties of the probability distribution function of the smeared scalar in this state are related to a quantum mechanical problem involving the Calogero-Sutherland Hamiltonian with a potential.

cond-mat↗

arXiv2003

What can the quantum liquid say on the brane black hole, the entropy of extremal black hole and the vacuum energy?

Using quantum liquids one can simulate the behavior of the quantum vacuum in the presence of the event horizon. The condensed matter analogs demonstrate that in most cases the quantum vacuum resists to formation of the horizon, and even if the horizon is formed different types of the vacuum instability develop, which are faster than the process of Hawking radiation. Nevertheless, it is possible to create the horizon on the quantum-liquid analog of the brane, where the vacuum life-time is long enough to consider the horizon as the quasistationary object. Using this analogy we calculate the Bekenstein entropy of the nearly extremal and extremal black holes, which comes from the fermionic microstates in the region of the horizon -- the fermion zero modes. We also discuss how the cancellation of the large cosmological constant follows from the thermodynamics of the vacuum.

gr-qc↗

arXiv2002

Thermodynamics and Self-Gravitating Systems

This work assembles some basic theoretical elements on thermal equilibrium, stability conditions, and fluctuation theory in self-gravitating systems illustrated with a few examples. Thermodynamics deals with states that have settled down after sufficient time has gone by. Time dependent phenomena are beyond the scope of this paper. While thermodynamics is firmly rooted in statistical physics, equilibrium configurations, stability criteria and the destabilizing effect of fluctuations are all expressed in terms of thermodynamic functions. The work is not a review paper but a pedagogical introduction which may interest theoreticians in astronomy and astrophysicists. It contains sufficient mathematical details for the reader to redo all calculations. References are only to seminal works or readable reviews. (Except in the ultimate sub-section.) Delicate mathematical problems are mentioned but are not discussed in detail.

astro-ph↗

arXiv2003

Rotational invariance and the spin-statistics theorem

In this article the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This is referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of this coupling while the Bose-Einstein follows by breaking it. In section 5, the above approach is related to Pauli's original spin-statistics theorem and finally in the last two sections, a theoretical justification, based on Clebsch-Gordan coefficients and the experimental evidence respectively, is presented.

quant-ph↗

arXiv1995

Fluctuating Membranes with Tilt Order

Thermal fluctuations are important for amphiphilic bilayer membranes since typical bending stiffnesses can be a few $k_B T$. The rod-like constituent molecules are generically tilted with respect to the local normal for packing reasons. We study the effects of fluctuations on membranes with nematic order, a simplified idealization with the same novel features as realistic tilt order. We find that nematic membranes lie in the same universality class as hexatic membranes, {\it i.e.} the couplings that distinguish nematic from hexatic order are marginally irrelevant. Our calculation also illustrates the advantages of conformal gauge, which brings great conceptual and technical simplifications compared to the more popular Monge gauge.

cond-mat↗

arXiv1995

Dynamics of quantum spin systems in dimer and valence-bond solid ground states stabilized by competing interactions

For special coupling ratios, the one-dimensional (1D) s=1/2 Heisenberg model with antiferromagnetic nearest and next-nearest neighbor interactions has a pure dimer ground state, and the 1D s=1 Heisenberg model with antiferromagnetic bilinear and biquadratic interactions has an exact valence-bond-solid ground state. The recursion method is used to calculate the T=0 spin dynamic structure factor for both models and, for the s=1/2 model, also the dimer dynamic structure factor. New results for line shapes and dynamically relevant dispersions are obtained.

cond-mat↗

arXiv1995

Thermodynamics of Finite Quantum Systems: Application to Spin Magnetism II

We extend our study of thermodynamics of a Kubo particle to temperatures smaller than the interlevel spacing. We obtain the distribution functions of spin susceptibility and heat capacity for Poisson and Wigner-Dyson level statistics. We evaluate the line shape of the Knight shift due to spin effects both in a single particle and for the ensemble average and compare it with orbital and spin-orbit contributions.

cond-mat↗

arXiv1993

Nonequilibrium Dynamics and Aging in the Three--Dimensional Ising Spin Glass Model

The low temperature dynamics of the three dimensional Ising spin glass in zero field with a discrete bond distribution is investigated via MC simulations. The thermoremanent magnetization is found to decay algebraically and the temperature dependent exponents agree very well with the experimentally determined values. The nonequilibrium autocorrelation function $C(t,t_w)$ shows a crossover at the waiting (or {\em aging}) time $t_w$ from algebraic {\em quasi-equilibrium} decay for times $t$$\ll$$t_w$ to another, faster algebraic decay for $t$$\gg$$t_w$ with an exponent similar to one for the remanent magnetization.

cond-mat↗

arXiv1993

Yang-Baxter equation in spin chains with long range interactions

We consider the $ su(n) $ spin chains with long range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities and we diagonalize them.

hep-th↗

arXiv1993

Transitions In Spectral Statistics

We present long range statistical properties of a recently introduced unitary random matrix ensemble, whose short range correlations were found to describe a transition from Wigner to Poisson type as a function of a single parameter.

cond-mat↗

arXiv1995

Surface crossover exponent for branched polymers in two dimensions

Transfer-matrix methods on finite-width strips with free boundary conditions are applied to lattice site animals, which provide a model for randomly branched polymers in a good solvent. By assigning a distinct fugacity to sites along the strip edges, critical properties at the special (adsorption) and ordinary transitions are assessed. The crossover exponent at the adsorption point is estimated as $ϕ= 0.505 \pm 0.015$, consistent with recent predictions that $ϕ= 1/2$ exactly for all space dimensionalities.

cond-mat↗

arXiv1996

Directed percolation near a wall

Series expansion methods are used to study directed bond percolation clusters on the square lattice whose lateral growth is restricted by a wall parallel to the growth direction. The percolation threshold $p_c$ is found to be the same as that for the bulk. However the values of the critical exponents for the percolation probability and mean cluster size are quite different from those for the bulk and are estimated by $β_1 = 0.7338 \pm 0.0001$ and $γ_1 = 1.8207 \pm 0.0004$ respectively. On the other hand the exponent $Δ_1=β_1 +γ_1$ characterising the scale of the cluster size distribution is found to be unchanged by the presence of the wall. The parallel connectedness length, which is the scale for the cluster length distribution, has an exponent which we estimate to be $ν_{1\parallel} = 1.7337 \pm 0.0004$ and is also unchanged. The exponent $τ_1$ of the mean cluster length is related to $β_1$ and $ν_{1\parallel}$ by the scaling relation $ν_{1\parallel} = β_1 + τ_1$ and using the above estimates yields $τ_1 = 1$ to within the accuracy of our results. We conjecture that this value of $τ_1$ is exact and further support for the conjecture is provided by the direct series expansion estimate $τ_1= 1.0002 \pm 0.0003$.

cond-mat↗

arXiv2000

Macroscopic Quantum Phase Interference in Antiferromagnetic Particles

The tunnel splitting in biaxial antiferromagnetic particles is studied with a magnetic field applied along the hard anisotropy axis. We observe the oscillation of tunnel splitting as a function of the magnetic field due to the quantum phase interference of two tunneling paths of opposite windings. The oscillation is similar to the recent experimental result with Fe}$_8$\textrm{\ molecular clusters.}

cond-mat↗

arXiv1993

Charge-Spin Separation and the Spectral Properties of Luttinger Liquids

We compute the spectral function rho(q,omega) of the one- dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. Charge-spin separation shows up in finite spectral weight at frequencies between v_sigma * q and v_rho * q where v_rho and v_sigma are the velocities of charge and spin fluctuations while spectral weight above v_rho * q and below -v_rho * q is generated by the hybridization of the Fermi surface at +/-k_F by interactions. There are nonuniversal power-law singularities at these special frequencies. We discuss the consistency of recent photoemission experiments on low-dimensional conductors with a Luttinger liquid picture which then would suggest very strong long- range interactions. It is pointed out that many-particle correlation functions in principle exhibit similar singularities but they probe different and complementary aspects of the Fermi surface interactions.

cond-mat↗

arXiv1995

Broken rotation symmetry in the fractional quantum Hall system

We demonstrate that the two-dimensonal electron system in a strong perpendicular magnetic field has stable states which break rotational but not translational symmetry. The Laughlin fluid becomes unstable to these states in quantum wells whose thickness exceeds a critical value which depends on the electron density. The order parameter at 1/3 reduced density resembles that of a nematic liquid crystal, in that a residual two-fold rotation axis is present in the low symmetry phase. At filling factors 1/5 and 1/7, there are states with four- and six-fold axes, as well. We discuss the experimental detection of these phases.

cond-mat↗