Beyond quantum microcanonical statistics

Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to consider the time evolution according to the unitary Schr\"odinger equation. On the other hand a mixed state, i.e. a statistical density matrix, is the standard formalism to account for thermal equilibrium, as postulated in the microcanonical quantum statistics. In the present paper an alternative treatment relying on a statistical analysis of the possible wavefunctions of an isolated system is presented. In analogy with the classical ergodic theory, the time evolution of the wavefunction determines the probability distribution in the phase space pertaining to an isolated system. However, this alone cannot account for a well defined thermodynamical description of the system in the macroscopic limit, unless a suitable probability distribution for the quantum constants of motion is introduced. We present a workable formalism assuring the emergence of typical values of thermodynamic functions, such as the internal energy and the entropy, in the large size limit of the system. This allows the identification of macroscopic properties independently of the specific realization of the quantum state. A description of material systems in agreement with equilibrium thermodynamics is then derived without constraints on the physical constituents and interactions of the system. Furthermore, the canonical statistics is recovered in all generality for the reduced density matrix of a subsystem

Tasting edge effects

We show that the baking of potato wedges constitutes a crunchy example of edge effects, which are usually demonstrated in electrostatics. A simple model of the diffusive transport of water vapor around the potato wedges shows that the water vapor flux diverges at the sharp edges in analogy with its electrostatic counterpart. This increased evaporation at the edges leads to the crispy taste of these parts of the potatoes.Comment: to appear in American Journal of Physic

Calculating Non-adiabatic Pressure Perturbations during Multi-field Inflation

Isocurvature perturbations naturally occur in models of inflation consisting of more than one scalar field. In this paper we calculate the spectrum of isocurvature perturbations generated at the end of inflation for three different inflationary models consisting of two canonical scalar fields. The amount of non-adiabatic pressure present at the end of inflation can have observational consequences through the generation of vorticity and subsequently the sourcing of B-mode polarisation. We compare two different definitions of isocurvature perturbations and show how these quantities evolve in different ways during inflation. Our results are calculated using the open source Pyflation numerical package which is available to download.Comment: v2: Typos fixed, references and comments added; v1: 8 pages, 10 figures, software available to download at http://pyflation.ianhuston.ne

Negative effective mass transition and anomalous transport in power-law hopping bands

We study the stability of spinless Fermions with power law hopping $H_{ij} \propto |i - j|^{-\alpha}$. It is shown that at precisely $\alpha_c =2$, the dispersive inflection point coalesces with the band minimum and the charge carriers exhibit a transition into negative effective mass regime, $m_\alpha^* < 0$ characterized by retarded transport in the presence of an electric field. Moreover, bands with $\alpha < 2$ must be accompanied by counter-carriers with $m_\alpha^* > 0$, having a positive band curvature, thus stabilizing the system in order to maintain equilibrium conditions and a proper electrical response. We further examine the semi-classical transport and response properties, finding an infrared divergent conductivity for 1/r hopping($\alpha =1$). The analysis is generalized to regular lattices in dimensions $d$ = 1, 2, and 3.Comment: 6 pages. 2 figure

Impurity states in graphene with intrinsic spin-orbit interaction

We consider the problem of electron energy states related to strongly localized potential of a single impurity in graphene. Our model simulates the effect of impurity atom substituting the atom of carbon, on the energy spectrum of electrons near the Dirac point. We take into account the internal spin-orbit interaction, which can modify the structure of electron bands at very small neighborhood of the Dirac point, leading to the energy gap. This makes possible the occurrence of additional impurity states in the vicinity of the gap.Comment: 10 pages, 5 figure

On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk

Dirac hamiltonian on the Poincare disk in the presence of an Aharonov-Bohm flux and a uniform magnetic field admits a one-parameter family of self-adjoint extensions. We determine the spectrum and calculate the resolvent for each element of this family. Explicit expressions for Green functions are then used to find Fredholm determinant representations for the tau function of the Dirac operator with two branch points on the Poincare disk. Isomonodromic deformation theory for the Dirac equation relates this tau function to a one-parameter class of solutions of the Painleve VI equation with $\gamma=0$. We analyze long distance behaviour of the tau function, as well as the asymptotics of the corresponding Painleve VI transcendents as $s\to 1$. Considering the limit of flat space, we also obtain a class of solutions of the Painleve V equation with $\beta=0$.Comment: 38 pages, 5 figure

Elliptical instability of a rapidly rotating, strongly stratified fluid

The elliptical instability of a rotating stratified fluid is examined in the regime of small Rossby number and order-one Burger number corresponding to rapid rotation and strong stratification. The Floquet problem describing the linear growth of disturbances to an unbounded, uniform-vorticity elliptical flow is solved using exponential asymptotics. The results demonstrate that the flow is unstable for arbitrarily strong rotation and stratification; in particular, both cyclonic and anticyclonic flows are unstable. The instability is weak, however, with growth rates that are exponentially small in the Rossby number. The analytic expression obtained for the growth rate elucidates its dependence on the Burger number and on the eccentricity of the elliptical flow. It explains in particular the weakness of the instability of cyclonic flows, with growth rates that are only a small fraction of those obtained for the corresponding anticyclonic flows. The asymptotic results are confirmed by numerical solutions of Floquet problem.Comment: 17 page

Lifshitz-like systems and AdS null deformations

Following arXiv:1005.3291 [hep-th], we discuss certain lightlike deformations of $AdS_5\times X^5$ in Type IIB string theory sourced by a lightlike dilaton $\Phi(x^+)$ dual to the N=4 super Yang-Mills theory with a lightlike varying gauge coupling. We argue that in the case where the $x^+$-direction is noncompact, these solutions describe anisotropic 3+1-dim Lifshitz-like systems with a potential in the $x^+$-direction generated by the lightlike dilaton. We then describe solutions of this sort with a linear dilaton. This enables a detailed calculation of 2-point correlation functions of operators dual to bulk scalars and helps illustrate the spatial structure of these theories. Following this, we discuss a nongeometric string construction involving a compactification along the $x^+$-direction of this linear dilaton system. We also point out similar IIB axionic solutions. Similar bulk arguments for $x^+$-noncompact can be carried out for deformations of $AdS_4\times X^7$ in M-theory.Comment: Latex, 20pgs, 1 eps fig; v2. references added; v3. minor clarifications added, to appear in PR

Stability of patterns with arbitrary period for a Ginzburg-Landau equation with a mean field

We consider the following system of equations A_t= A_{xx} + A - A^3 -AB,\quad x\in R,\,t>0, B_t = \sigma B_{xx} + \mu (A^2)_{xx}, x\in R, t>0, where \mu > \sigma >0. It plays an important role as a Ginzburg-Landau equation with a mean field in several fields of the applied sciences. We study the existence and stability of periodic patterns with an arbitrary minimal period L. Our approach is by combining methods of nonlinear functional analysis such as nonlocal eigenvalue problems and the variational characterization of eigenvalues with Jacobi elliptic integrals. This enables us to give a complete characterization of existence and stability for all solutions with A>0, spatial average =0 and an arbitrary minimal period

Helical Symmetry in Linear Systems

We investigate properties of solutions of the scalar wave equation and Maxwell's equations on Minkowski space with helical symmetry. Existence of local and global solutions with this symmetry is demonstrated with and without sources. The asymptotic properties of the solutions are analyzed. We show that the Newman--Penrose retarded and advanced scalars exhibit specific symmetries and generalized peeling properties.Comment: 11 page