608 research outputs found
Classification of Perturbations for Membranes with Bending Rigidity
A complete classification of the renormalization-group flow is given for
impurity-like marginal operators of membranes whose elastic stress scales like
(\Delta r)^2 around the external critical dimension d_c=2. These operators are
classified by characteristic functions on R^2 x R^2.Comment: latex, 3 .eps-file
Dissipative Bose-Einstein condensation in contact with a thermal reservoir
We investigate the real-time dynamics of open quantum spin- or hardcore
boson systems on a spatial lattice, which are governed by a Markovian quantum
master equation. We derive general conditions under which the hierarchy of
correlation functions closes such that their time evolution can be computed
semi-analytically. Expanding our previous work [Phys. Rev. A 93, 021602 (2016)]
we demonstrate the universality of a purely dissipative quantum Markov process
that drives the system of spin- particles into a totally symmetric
superposition state, corresponding to a Bose-Einstein condensate of hardcore
bosons. In particular, we show that the finite-size scaling behavior of the
dissipative gap is independent of the chosen boundary conditions and the
underlying lattice structure. In addition, we consider the effect of a uniform
magnetic field as well as a coupling to a thermal bath to investigate the
susceptibility of the engineered dissipative process to unitary and nonunitary
perturbations. We establish the nonequilibrium steady-state phase diagram as a
function of temperature and dissipative coupling strength. For a small number
of particles , we identify a parameter region in which the engineered
symmetrizing dissipative process performs robustly, while in the thermodynamic
limit , the coupling to the thermal bath destroys any
long-range order.Comment: 30 pages, 8 figures; Revised version: Minor changes and references
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Instanton calculus for the self-avoiding manifold model
LaTeX+revtex4+eps figures. 129 pages. A few changes in the introduction section.We compute the normalisation factor for the large order asymptotics of perturbation theory for the self-avoiding manifold (SAM) model describing flexible tethered (D-dimensional) membranes in d-dimensional space, and the epsilon-expansion for this problem. For that purpose, we develop the methods inspired from instanton calculus, that we introduced in a previous publication (Nucl. Phys. B 534 (1998) 555), and we compute the functional determinant of the fluctuations around the instanton configuration. This determinant has UV divergences and we show that the renormalized action used to make perturbation theory finite also renders the contribution of the instanton UV-finite. To compute this determinant, we develop a systematic large-d expansion. For the renormalized theory, we point out problems in the interplay between the limits epsilon->0 and d->infinity, as well as IR divergences when epsilon= 0. We show that many cancellations between IR divergences occur, and argue that the remaining IR-singular term is associated to amenable non-analytic contributions in the large-d limit when epsilon= 0. The consistency with the standard instanton-calculus results for the self-avoiding walk is checked for D = 1
Large Orders for Self-Avoiding Membranes
We derive the large order behavior of the perturbative expansion for the
continuous model of tethered self-avoiding membranes. It is controlled by a
classical configuration for an effective potential in bulk space, which is the
analog of the Lipatov instanton, solution of a highly non-local equation. The
n-th order is shown to have factorial growth as (-cst)^n (n!)^(1-epsilon/D),
where D is the `internal' dimension of the membrane and epsilon the engineering
dimension of the coupling constant for self-avoidance. The instanton is
calculated within a variational approximation, which is shown to become exact
in the limit of large dimension d of bulk space. This is the starting point of
a systematic 1/d expansion. As a consequence, the epsilon-expansion of
self-avoiding membranes has a factorial growth, like the epsilon-expansion of
polymers and standard critical phenomena, suggesting Borel summability.
Consequences for the applicability of the 2-loop calculations are examined.Comment: 40 pages Latex, 32 eps-files included in the tex
Polymers and manifolds in static random flows: a renormalization group study
We study the dynamics of a polymer or a D-dimensional elastic manifold
diffusing and convected in a non-potential static random flow (the ``randomly
driven polymer model''). We find that short-range (SR) disorder is relevant for
d < 4 for directed polymers (each monomer sees a different flow) and for d < 6
for isotropic polymers (each monomer sees the same flow) and more generally for
d<d_c(D) in the case of a manifold. This leads to new large scale behavior,
which we analyze using field theoretical methods. We show that all divergences
can be absorbed in multilocal counter-terms which we compute to one loop order.
We obtain the non trivial roughness zeta, dynamical z and transport exponents
phi in a dimensional expansion. For directed polymers we find zeta about 0.63
(d=3), zeta about 0.8 (d=2) and for isotropic polymers zeta about 0.8 (d=3). In
all cases z>2 and the velocity versus applied force characteristics is
sublinear, i.e. at small forces v(f) f^phi with phi > 1. It indicates that this
new state is glassy, with dynamically generated barriers leading to trapping,
even by a divergenceless (transversal) flow. For random flows with long-range
(LR) correlations, we find continuously varying exponents with the ratio gL/gT
of potential to transversal disorder, and interesting crossover phenomena
between LR and SR behavior. For isotropic polymers new effects (e.g. a sign
change of zeta - zeta_0) result from the competition between localization and
stretching by the flow. In contrast to purely potential disorder, where the
dynamics gets frozen, here the dynamical exponent z is not much larger than 2,
making it easily accessible by simulations. The phenomenon of pinning by
transversal disorder is further demonstrated using a two monomer ``dumbbell''
toy model.Comment: Final version, some explications added and misprints corrected (69
pages latex, 40 eps-figures included
Random RNA under tension
The Laessig-Wiese (LW) field theory for the freezing transition of random RNA
secondary structures is generalized to the situation of an external force. We
find a second-order phase transition at a critical applied force f = f_c. For f
f_c, the extension L as a function of
pulling force f scales as (f-f_c)^(1/gamma-1). The exponent gamma is calculated
in an epsilon-expansion: At 1-loop order gamma = epsilon/2 = 1/2, equivalent to
the disorder-free case. 2-loop results yielding gamma = 0.6 are briefly
mentioned. Using a locking argument, we speculate that this result extends to
the strong-disorder phase.Comment: 6 pages, 10 figures. v2: corrected typos, discussion on locking
argument improve
The two general activation systems of affect: Structural findings, evolutionary considerations, and psychobiological evidence
D. Watson and A. Tellegen (19X5') proposed a "consensual " structure of affect based on J. A. Russell's (1980) circumplcx. The authors " review of the literature indicates that this 2-factor model captures robust structural properties of self-rated mood. Nevertheless, the evidence also indicates that the circumplcx does not fit the data closely and needs to be refined. Most notably, the model's dimensions are not entirely independent: moreover, with the exception of Pleasantness—Unpleasantness, they are not completely bipolar. More generally, the data suggest a model that falls somewhere between classic simple structure and a true circumplex. The authors then examine two of the dimensions imbedded in this structure, which they label Negative Activation (NA) and Positive Activation (PA). The authors argue that PA and NA represent the subjective components of broader biobchavioral systems of approach and withdrawal, respectively. The authors conclude by demonstrating how this framework helps to clarify various affect-related phenomena, including circadian rhythms, sleep, and the mood disorders. On the basis of a review and reanalysis of the existing data, Watson and Tellegen (1985) concluded that "a basic twodimensional structure of affect emerges across a number of different lines of research and a very large number of analyses " (p. 234)
Interacting crumpled manifolds
In this article we study the effect of a delta-interaction on a polymerized
membrane of arbitrary internal dimension D. Depending on the dimensionality of
membrane and embedding space, different physical scenarios are observed. We
emphasize on the difference of polymers from membranes. For the latter,
non-trivial contributions appear at the 2-loop level. We also exploit a
``massive scheme'' inspired by calculations in fixed dimensions for scalar
field theories. Despite the fact that these calculations are only amenable
numerically, we found that in the limit of D to 2 each diagram can be evaluated
analytically. This property extends in fact to any order in perturbation
theory, allowing for a summation of all orders. This is a novel and quite
surprising result. Finally, an attempt to go beyond D=2 is presented.
Applications to the case of self-avoiding membranes are mentioned
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