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arXiv2001

Dynamic Critical Phenomena in Trapped Bose Gases

Nonlinear dynamics of a trapped Bose-Einstein condensate, subject to the action of a resonant external field, is studied. This field produces a spatio-temporal modulation of the trapping potential with the frequency close to the transition frequency between the ground state and a higher energy level. The evolution equations of fractional populations display a kind of critical phenomena at a critical line on the manifold of the system parameters. It is demonstrated that there exists a direct analogy between dynamical instability at this line and critical phenomena at a critical line of a related averaged system.

cond-mat↗

arXiv1995

Evidence for charge-flux duality near the quantum Hall liquid to insulator transition

We examine the longitudinal, non-linear, current-voltage characteristics near the quantum Hall liquid to insulator transition and show that a simple mapping exists between the characteristics on the quantum Hall side and those on the insulating side of the transition. More precisely, at filling factors related by the law of corresponding states the current and voltage simply trade places. We interpret these observations as evidence for the existence, in the composite boson description, of charge-flux duality near disorder dominated transitions in quantum Hall systems. (Appearances notwithstanding, this is an experimental paper.)

cond-mat↗

arXiv1998

Critical Velocity in 3He-B Vibrating Wire Experiments as Analog of Vacuum Instability in a Slowly Oscillating Electric Field

The Lancaster experiments with a cylindrical wire moving in superfluid 3He-B are discussed, where the measured critical velocity of pair creation is much below the Landau critical velocity. The phenomenon is shown to be analogous to the instability of the electron-positron vacuum in an adiabatically alternating strong electric potential of both signs, where the positive- and negative-root levels cross and thus the instability treshold is twice less than in the conventional case of a single static potential well.

cond-mat↗

arXiv1995

Ginzburg-Landau Expansion and the Slope of the Upper Critical Field in Disordered Superconductors with Anisotropic Pairing

It is demonstrated that the slope of the upper critical field $|dH_{c2}/dT|_{T_{c}}$ in superconductors with $d$-wave pairing drops rather fast with concentration of normal impurities, while in superconductors with anisotropic $s$-wave pairing $|dH_{c2}/dT|_{T_{c}}$ grows, and in the limit of strong disorder is described by the known dependences of the theory of ``dirty'' superconductors. This allows to use the measurements of $H_{c2}$ in disordered superconductors to discriminate between these different types of pairing in high-temperature and heavy-fermion superconductors.

cond-mat↗

arXiv2001

CP_N Solitons in Quantum Hall Systems

We will present here an elementary pedagogical introduction to $CP_N$ solitons in quantum Hall systems. We begin with a brief introduction to both $CP_N$ models and to quantum Hall (QH) physics. Then we focus on spin and layer-spin degrees of freedom in QH systems and point out that these are in fact $CP_N$ fields for N=1 and N=3. Excitations in these degrees of freedom will be shown to be topologically non-trivial soliton solutions of the corresponding $CP_N$ field equations. This is followed by a brief summary of our own recent work in this area, done with Sankalpa Ghosh. [ Invited Plenary Lecture at the International Conference on Geometry, Integrability and Nonlinearity in Condensed Matter & Soft Condensed Matter Physics held at Bansko, Bulgaria, July 15-20, 2001. ]

cond-mat↗

arXiv2002

Loading of a cold atomic beam into a magnetic guide

We demonstrate experimentally the continuous and pulsed loading of a slow and cold atomic beam into a magnetic guide. The slow beam is produced using a vapor loaded laser trap, which ensures two-dimensional magneto-optical trapping, as well as cooling by a moving molasses along the third direction. It provides a continuous flux larger than $10^9$ atoms/s with an adjustable mean velocity ranging from 0.3 to 3 m/s, and with longitudinal and transverse temperatures smaller than $100 μ$K. Up to $3 10^8$ atoms/s are injected into the magnetic guide and subsequently guided over a distance of 40 cm.

cond-mat↗

arXiv1993

Quantum Antiferromagnets in Two Dimensions

These are lectures presented at the summer course on ``Low Dimensional Quantum Field Theories for Condensed Matter Physicists'', 24 Aug. to 4 Sep. 1992, Trieste, Italy. I review recent work, performed in collaboration primarily with N. Read and Jinwu Ye, on the properties of quantum antiferromagnets in two dimensions. The emphasis is on the properties of the antiferromagnet in states which do not have any long-range magnetic order. The universal spin dynamics in the quantum critical region of number of frustrated and random antiferromagnets is studied; implications for neutron scattering experiments in the lightly-doped cuprates are noted. The nature of the quantum-disordered phase of non-random frustrated antiferromagnets is examined in some detail: the states found have ({\em i\/}) collinear spin correlations, spin-Peierls or valence-bond-solid order, and confined spinons, order and confined spinons or ({\em ii\/}) coplanar spin correlations, no spin-Peierls order and deconfined bosonic spinons.

cond-mat↗

arXiv2000

Waveguides coupled through a semitransparent barrier: a Birman-Schwinger analysis

The paper is devoted to a model of a mesoscopic system consisting of a pair of parallel planar waveguides separated by an infinitely thin semitransparent boundary modeled by a transverse delta interaction. We develop the Birman-Schwinger theory for the corresponding generalized Schroedinger operator. The spectral properties become nontrivial if the barrier coupling is not invariant with respect to longitudinal translations, in particular, there are bound states if the barrier is locally more transparent in the mean and the coupling parameter reaches the same asymptotic value in both directions along the guide axis. We derive the weak-coupling expansion of the ground-state eigenvalue for the cases when the perturbation is small in the supremum and the L^1-norms. The last named result applies to the situation when the support of the leaky part shrinks: the obtained asymptotics differs from that of a double guide divided by a pierced Dirichlet barrier. We also derive an upper bound on the number of bound states.

math-ph↗

arXiv2004

Strong-coupling asymptotic expansion for Schrödinger operators with a singular interaction supported by a curve in $\mathbb{R}^3$

We investigate a class of generalized Schrödinger operators in $L^2(\mathbb{R}^3)$ with a singular interaction supported by a smooth curve $Γ$. We find a strong-coupling asymptotic expansion of the discrete spectrum in case when $Γ$ is a loop or an infinite bent curve which is asymptotically straight. It is given in terms of an auxiliary one-dimensional Schrödinger operator with a potential determined by the curvature of $Γ$. In the same way we obtain an asymptotics of spectral bands for a periodic curve. In particular, the spectrum is shown to have open gaps in this case if $Γ$ is not a straight line and the singular interaction is strong enough.

math-ph↗

arXiv2001

A simple solid-on-solid model of epitaxial film growth: submonolayer substrate coverage

In this work we investigate influence of substrate temperature on the surface morphology for substrate coverage below one monolayer. The model of film growth is based on random deposition enriched by limited surface diffusion. Also anisotropy in the growth is involved. We found from computer simulations for simple cubic lattice and solid-on-solid model, that the surface morphology changes with increasing temperature from isotropically distributed isolated small islands, through anisotropic 1-D stripes to larger 2-D anisotropic islands and again randomly distributed single atoms. The transition is also marked in height-height correlation function dependence on temperature, as directly seen by snapshots from simulations. The results are in good qualitative agreement with already published results of kinetic Monte Carlo simulations, as well as with some experimental data.

cond-mat↗

arXiv2000

Boolean derivatives and computation of cellular automata

The derivatives of a Boolean function are defined up to any order. The Taylor and MacLaurin expansions of a Boolean function are thus obtained. The last corresponds to the ring sum expansion (RSE) of a Boolean function, and is a more compact form than the usual canonical disjunctive form. For totalistic functions the RSE allows the saving of a large number of Boolean operations. The algorithm has natural applications to the simulations of cellular automata using the multi site coding technique. Several already published algorithms are analized, and expressions with fewer terms are generally found.

cond-mat↗

arXiv1992

Fluctuating Interfaces, Surface Tension, and Capillary Waves: An Introduction

We present an introduction to modern theories of interfacial fluctuations and the associated interfacial parameters: surface tension and surface stiffness, as well as their interpretation within the capillary wave model. Transfer matrix spectrum properties due to fluctuation of an interface in a long-cylinder geometry are reviewed. The roughening transition and properties of rigid interfaces below the roughening temperature in 3d lattice models are surveyed with emphasis on differences in fluctuations and transfer matrix spectral properties of rigid vs. rough interfaces.

cond-mat↗

arXiv1994

Localization in Lattice Gauge Theory and a New Multigrid Method

We show numerically that the lowest eigenmodes of the 2-dimensional Laplace-operator with SU(2) gauge couplings are strongly localized. A connection is drawn to the Anderson-Localization problem. A new Multigrid algorithm, capable to deal with these modes, shows no critical slowing down for this problem.

hep-lat↗

arXiv1996

Power Laws are Logarithmic Boltzmann Laws

Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative dynamics might be the natural origin for the emergence of criticality and scale hierarchies without fine-tuning.

adap-org↗

arXiv1994

The Higgs model for anyons and Liouville action: Chaotic spectrum, energy gap and exclusion principle

Geodesic completness and self-adjointness imply that the Hamiltonian for anyons is the Laplacian with respect to the Weil-Petersson metric. This metric is complete on the Deligne-Mumford compactification of moduli (configuration) space. The structure of this compactification fixes the possible anyon configurations. This allows us to identify anyons with singularities (elliptic points with ramification $q^{-1}$) in the Poincaré metric implying that anyon spectrum is chaotic for $n\ge 3$. Furthermore, the bound on the holomorphic sectional curvature of moduli spaces implies a gap in the energy spectrum. For $q=0$ (punctures) anyons are infinitely separated in the Poincaré metric (hard-core). This indicates that the exclusion principle has a geometrical intepretation. Finally we give the differential equation satisfied by the generating function for volumes of the configuration space of anyons.

hep-th↗

arXiv1995

Type II Anyon Superconductivity

Assuming that the superconductivity which is described by the low energy effective action of the anyon system may be type II, we discuss its characteristics. We also study physical properties of the Chern-Simons vortices, which may be formed as the external magnetic field is applied to the system, such as their statistics, the free energy of single vortex and the interaction energy between two vortices.

cond-mat↗

arXiv1996

Fusion & Tensoring of Conformal Field Theory and Composite Fermion Picture of Fractional Quantum Hall Effect

We propose a new way for describing the transition between two quantum Hall effect states with different filling factors within the framework of rational conformal field theory. Using a particular class of non-unitary theories, we explicitly recover Jain's picture of attaching flux quanta by the fusion rules of primary fields. Filling higher Landau levels of composite fermions can be described by taking tensor products of conformal theories. The usual projection to the lowest Landau level corresponds then to a simple coset of these tensor products with several U(1)-theories divided out. These two operations -- the fusion map and the tensor map -- can explain the Jain series and all other observed fractions as exceptional cases. Within our scheme of transitions we naturally find a field with the experimentally observed universal critical exponent 7/3.

hep-th↗

arXiv1994

Critical Temperature and Amplitude Ratios from a Finite-Temperature Renormalization Group

We study $ł\f^4$ theory using an environmentally friendly finite-temperature renormalization group. We derive flow equations, using a fiducial temperature as flow parameter, develop them perturbatively in an expansion free from ultraviolet and infrared divergences, then integrate them numerically from zero to temperatures above the critical temperature. The critical temperature, at which the mass vanishes, is obtained by integrating the flow equations and is determined as a function of the zero-temperature mass and coupling. We calculate the field expectation value and minimum of the effective potential as functions of temperature and derive some universal amplitude ratios which connect the broken and symmetric phases of the theory. The latter are found to be in good agreement with those of the three-dimensional Ising model obtained from high- and low-temperature series expansions.

hep-th↗