A particle in equilibrium with a bath realizes worldline supersymmetry

We study the relation between the partition function of a non--relativistic particle, in one spatial dimension, that describes the equilibrium fluctuations implicitly, and the partition function of the same system, deduced from the Langevin equation, that describes the fluctuations explicitly, of a bath with additive white--noise properties using Monte Carlo simulations for computing the correlation functions that satisfy the corresponding identities. We show that both can be related to the partition function of the corresponding, maximally supersymmetric, theory with one--dimensional bosonic worldvolume, by appropriate analytic continuation, from Euclidian to real time, and that they can all describe the same physics, since the correlation functions of the observables satisfy the same identities for all systems.The supersymmetric theory provides the consistent closure for describing the fluctuations. Therefore supersymmetry is relevant at the scale in which equilibrium with the bath is meaningful. At scales when the "true" degrees of freedom of the bath can be resolved (e.g. atoms and molecules for the case of thermal fluctuations) the superpartners become "hidden". They can be, always, revealed through the identities satisfied by the correlation functions of the appropriate noise field, however. In fact, the same formalism applies whatever the "microscopic" origin of the fluctuations. Therefore, all consistently closed physical systems are supersymmetric--and any system that is explicitly not invariant under supersymmetric transformations, is, in fact, open and, therefore, incomplete.Comment: 48 pages, many PNG figures, LaTeX2e. Requires utphys.bst for the bibliography. v2: Extensively rewritten; errors corrected regarding the "fermionic'' action and presentation clarified and sharpene

Short-lived lattice quasiparticles for strongly interacting fluids

It is shown that lattice kinetic theory based on short-lived quasiparticles proves very effective in simulating the complex dynamics of strongly interacting fluids (SIF). In particular, it is pointed out that the shear viscosity of lattice fluids is the sum of two contributions, one due to the usual interactions between particles (collision viscosity) and the other due to the interaction with the discrete lattice (propagation viscosity). Since the latter is {\it negative}, the sum may turn out to be orders of magnitude smaller than each of the two contributions separately, thus providing a mechanism to access SIF regimes at ordinary values of the collisional viscosity. This concept, as applied to quantum superfluids in one-dimensional optical lattices, is shown to reproduce shear viscosities consistent with the AdS-CFT holographic bound on the viscosity/entropy ratio. This shows that lattice kinetic theory continues to hold for strongly coupled hydrodynamic regimes where continuum kinetic theory may no longer be applicable.Comment: 10 pages, 2 figure

Lattice and Continuum Theories

We investigate path integral formalism for continuum theory. It is shown that the path integral for the soft modes can be represented in the form of a lattice theory. Kinetic term of this lattice theory has a standard form and potential term has additional nonlocal terms which contributions should tend to zero in the limit of continuum theory. Contributions of these terms can be estimated. It is noted that this representation of path integral may be useful to improve lattice calculations taking into account hard modes contribution by standard perturbative expansion. We discuss translation invariance of correlators and the possibility to construct a lattice theory which keeps rotary invariance also.Comment: (Latex, 6 pages), preprint CEBAF-TH-94-1

Relating Theories via Renormalization

The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is the outgrowth of one hundred and fifty years of scientific study of thermal physics and phase transitions. Different phases of matter show qualitatively different behavior separated by abrupt phase transitions. These qualitative differences seem to be present in experimentally observed condensed-matter systems. However, the "extended singularity theorem" in statistical mechanics shows that sharp changes can only occur in infinitely large systems. Abrupt changes from one phase to another are signaled by fluctuations that show correlation over infinitely long distances, and are measured by correlation functions that show algebraic decay as well as various kinds of singularities and infinities in thermodynamic derivatives and in measured system parameters. Renormalization methods were first developed in field theory to get around difficulties caused by apparent divergences at both small and large scales. The renormalization (semi-)group theory of phase transitions was put together by Kenneth G. Wilson in 1971 based upon ideas of scaling and universality developed earlier in the context of phase transitions and of couplings dependent upon spatial scale coming from field theory. Correlations among regions with fluctuations in their order underlie renormalization ideas. Wilson's theory is the first approach to phase transitions to agree with the extended singularity theorem. Some of the history of the study of these correlations and singularities is recounted, along with the history of renormalization and related concepts of scaling and universality. Applications are summarized.Comment: This note is partially a summary of a talk given at the workshop "Part and Whole" in Leiden during the period March 22-26, 201

Dynamical Evolution in Noncommutative Discrete Phase Space and the Derivation of Classical Kinetic Equations

By considering a lattice model of extended phase space, and using techniques of noncommutative differential geometry, we are led to: (a) the conception of vector fields as generators of motion and transition probability distributions on the lattice; (b) the emergence of the time direction on the basis of the encoding of probabilities in the lattice structure; (c) the general prescription for the observables' evolution in analogy with classical dynamics. We show that, in the limit of a continuous description, these results lead to the time evolution of observables in terms of (the adjoint of) generalized Fokker-Planck equations having: (1) a diffusion coefficient given by the limit of the correlation matrix of the lattice coordinates with respect to the probability distribution associated with the generator of motion; (2) a drift term given by the microscopic average of the dynamical equations in the present context. These results are applied to 1D and 2D problems. Specifically, we derive: (I) The equations of diffusion, Smoluchowski and Fokker-Planck in velocity space, thus indicating the way random walk models are incorporated in the present context; (II) Kramers' equation, by further assuming that, motion is deterministic in coordinate spaceComment: LaTeX2e, 40 pages, 1 Postscript figure, uses package epsfi

Simulating quantum mechanics on a quantum computer

Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quantum systems on a quantum computer with an exponential speedup compared to simulations on classical computers. Issues involved in simulating relativistic systems of Dirac and gauge particles are discussed.Comment: 22 pages LaTeX; Expanded version of a talk given by WT at the PhysComp '96 conference, BU, Boston MA, November 1996. Minor corrections made, references adde