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arXiv2001

High Pressure Insulator-Metal Transition in Molecular Fluid Oxygen

We report the first experimental evidence for a metallic phase in fluid molecular oxygen. Our electrical conductivity measurements of fluid oxygen under dynamic quasi-isentropic compression show that a non-metal/metal transition occurs at 3.4 fold compression, 4500 K and 1.2 Mbar. We discuss the main features of the electrical conductivity dependence on density and temperature and give an interpretation of the nature of the electrical transport mechanisms in fluid oxygen at these extreme conditions.

cond-mat↗

arXiv2000

Freezing of dynamical exponents in low dimensional random media

A particle in a random potential with logarithmic correlations in dimensions $d=1,2$ is shown to undergo a dynamical transition at $T_{dyn}>0$. In $d=1$ exact results demonstrate that $T_{dyn}=T_c$, the static glass transition temperature, and that the dynamical exponent changes from $z(T)=2 + 2 (T_c/T)^2$ at high temperature to $z(T)= 4 T_c/T$ in the glass phase. The same formulae are argued to hold in $d=2$. Dynamical freezing is also predicted in the 2D random gauge XY model and related systems. In $d=1$ a mapping between dynamics and statics is unveiled and freezing involves barriers as well as valleys. Anomalous scaling occurs in the creep dynamics.

cond-mat↗

arXiv2002

Critical phenomena of thick branes in warped spacetimes

We have investigated the effects of a generic bulk first-order phase transition on thick Minkowski branes in warped geometries. As occurs in Euclidean space, when the system is brought near the phase transition an interface separating two ordered phases splits into two interfaces with a disordered phase in between. A remarkable and distinctive feature is that the critical temperature of the phase transition is lowered due to pure geometrical effects. We have studied a variety of critical exponents and the evolution of the transverse-traceless sector of the metric fluctuations.

hep-th↗

arXiv2001

New phasing method based on the principle of minimum charge

A new method of the phase determination in X-ray crystallography is proposed. The method is based on the so-called "minimum charge" principle, recently suggested by Elser. The electron density function $ρ$ is sought in the form $ρ({\bf x})=|ψ({\bf x})|^2$, where $ψ$ is an $n{-component}$ real function. The norm $\int|ψ({\bf x})|^2 d{\bf x}$ is minimized under the constraint imposed by the measured data on the amplitudes of Fourier harmonics of $ρ$. Compared to the straightforward implementation of the "minimum charge" scheme, the method attenuates the Gibbs phenomenon and is also capable of extrapolation of the diffraction data beyond the set of measured amplitudes. The method is applicable to quasicrystals under the condition that the number of components $n$ of the function $ψ$ is bigger than the dimensionality of the ``atomic surface''. It is successfully tested on synthetic data for Fibonacci chain and the octagonal tiling. In the latter case the reconstructed density map shows the shape of the atomic surface, despite relatively low data resolution.

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↗

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

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↗

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↗

arXiv1992

Second-Order Dynamics in the Collective Evolution of Coupled Maps and Automata

We review recent numerical studies and the phenomenology of spatially synchronized collective states in many-body dynamical systems. These states exhibit thermodynamic noise superimposed on the collective, quasiperiodic order parameter evolution with typically one basic irrational frequency. We concentrate on the description of the global temporal properties in terms of second-order difference equations.

cond-mat↗

arXiv1996

Partially Solvable Anisotropic t-J Model with Long-Range Interactions

A new anisotropic t-J model in one dimension is proposed which has long-range hopping and exchange. This t-J model is only partially solvable in contrast to known integrable models with long-range interaction. In the high-density limit the model reduces to the XXZ chain with the long-range exchange. Some exact eigenfunctions are shown to be of Jastrow-type if certain conditions for an anisotropy parameter are satisfied. The ground state as well as the excitation spectrum for various cases of the anisotropy parameter and filling are derived numerically. It is found that the Jastrow-type wave function is an excellent trial function for any value of the anisotropy parameter.

cond-mat↗

arXiv1995

Detection of pairing from the extended Aharonov-Bohm period in strongly correlated electron systems

Inspired from Sutherland's work [Phys. Rev. Lett. {\bf 74}, 816 (1995)] on detecting bound spin waves, we propose that bound electron states can be detected from the dependence of interacting electron systems to the Aharonov-Bohm flux in the `extended zone' scheme, where the electron pairing halves the original period $N_a$ flux quanta in a system of linear size $N_a$. Along with the Bethe-ansatz analysis, a numerical implementation for keeping track of the adiabatic flow of energy levels is applied to the attractive/repulsive Hubbard models and the $t-J$ ladder.

cond-mat↗

arXiv1995

Spin Gap of Two-Dimensional Antiferromagnet Representing CaV$_4$O$_9$

We examined a two-dimensional Heisenberg model with two kinds of exchange energies, $J_e$ and $J_c$. This model describes localized spins at vanadium ions in a layer of CaV$_4$O$_9$, for which a spin gap is found by a recent experiment. Comparing the high temperature expansion of the magnetic susceptibility to experimental data, we determined the exchange energies as $J_e \simeq$ 610 K and $J_c \simeq$ 150 K. By the numerical diagonalization we estimated the spin gap as $Δ\sim 0.2J_e \simeq$ 120 K, which consists with the experimental value 107 K. Frustration by finite $J_c$ enhances the spin gap.

cond-mat↗

arXiv1995

Hidden Orders and RVB Formation of the Four-Leg Heisenberg Ladder Model

The ground state of the four-chain Heisenberg ladder model is numerically investigated. Hidden-order correlations suitable for the system are introduced and calculated with an emphasis on the spatially isotropic point, where a corresponding material exists. The existence of a long-range hidden correlation indicates formation of a short-range RVB state in the case of the antiferromagnetic inter-chain coupling. A transition between the phase of the ferromagnetic inter-chain coupling and that of the antiferromagnetic one is discussed.

cond-mat↗

arXiv1995

Haldane Gap and Hidden Order in the S=2 Antiferromagnetic Quantum Spin Chain

We have investigated Haldane's conjecture for the S=2 isotropic antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm for chains up to L=350 spins, we find in the thermodynamic limit a finite spin gap of Delta = 0.085(5)J and a finite spin-spin correlation length xi = 49(1) lattice spacings. We establish the ground state energy per bond to be E_0=-4.761248(1)J. We show that the ground state has a hidden topological order that is revealed in a nonlocal string correlation function. This means that the physics of the S=2 chain can be captured by a valence-bond solid description. We also observe effective free spin-1 states at the ends of an open S=2 chain.

cond-mat↗