arXiv subjects

B. L. Altshuler

Publications and source records attributed to B. L. Altshuler.

At least 127 records · Page 7Linked to original sources

arXiv1996

Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory

The Bohigas--Giannoni--Schmit conjecture stating that the statistical spectral properties of systems which are chaotic in their classical limit coincide with random matrix theory is proved. For this purpose a new semiclassical field theory for individual chaotic systems is constructed in the framework of the non--linear $σ$-model. The low lying modes are shown to be associated with the Perron--Frobenius spectrum of the underlying irreversible classical dynamics. It is shown that the existence of a gap in the Perron-Frobenius spectrum results in a RMT behavior. Moreover, our formalism offers a way of calculating system specific corrections beyond RMT.

cond-mat↗

arXiv1995

The Problem of Classical Limit in Quantum Cosmology: The effective action language

The tool of functional averaging over some ``large'' diffeomorphisms is used to describe quantum systems with constraints, in particular quantum cosmology, in the language of quantum Effective Action. Simple toy models demonstrate a supposedly general phenomenon: the presence of a constraint results in ``quantum repel'' from the classical mass shell.

gr-qc↗

arXiv1995

Random Matrix Model and the Calogero-Sutherland Model: A Novel Current-Density Mapping

We investigate the relation between the invariant correlators of random matrix theory and correlators of the integrable one-dimensional systems. Starting from the relation between correlators for the coupling strengths $λ=1/ 2$, $1$, and $2$, we explore the local current-density mapping applicable to arbitrary $λ$ including {\em irrational\/} values, which results from the novel structure of the Calogero-Sutherland model. We find an interesting and novel relationship between equal time current and density correlations for any coupling, which exist {\em in addition} to the usual Ward Identities for this class of systems.

cond-mat↗

arXiv1995

Giant Microwave Absorption in Metallic Grains: Relaxation Mechanism

We show that the low frequency microwave absorption of an ensemble of small metallic grains at low temperatures is dominated by a mesoscopic relaxation mechanism. Giant positive magnetoresistance and very strong temperature dependence of the microwave conductivity is predicted.

cond-mat↗

arXiv1995

Spectral Correlation and Response functions in Quantum Dots

We derive a general relation between correlators of density of states fluctuations and density response functions. It applies equally to quantum chaotic systems of pure symmetry (unitary, orthogonal, and symplectic) as well as to the crossover region between the universality classes. This relation is much more robust than Wigner-Dyson statistics; its validity extends to disordered metals with finite conductance and even to the Anderson insulators with large localization length.

cond-mat↗

arXiv1995

Theory of the Spin Gap in High Temperature Superconductors

We analyze pairing in two dimensional spin liquids. We argue that interplane pairing enhanced by magnetic correlations is the most plausible explanation of the spin gap phenomenon observed in underdoped cuprates. The details of the pairing theory depend on the in-plane antiferromagnetic correlations. We consider two models: $2p_F$ correlations induced by a strong gauge field interaction and undamped spin waves. We estimate the pairing temperature $T_s$ and the angular dependence of the gap function and discuss physical consequences.

cond-mat↗

arXiv1995

The $\bf T=0$ $\bf 2k_F$ density wave phase transition in a two dimensional Fermi liquid is first order

We study $T=0$ spin density wave transitions in two dimensional Fermi liquids in which the ordering wavevector $\bf Q$ is such that the tangents to the Fermi line at the points connected by $\bf Q$ are parallel (e.g. $Q=2p_F$ in a system with a circular Fermi line) and the Fermi line is not flat. We show that the transition is first order if the ordering wave vector $\bf Q$ is not commensurate with a reciprocal lattice vector, $\bf G$, i.e. ${\bf Q} \neq {\bf G}/2$. If $\bf Q$ is close to ${\bf G}/2$ the transition is weakly first order and an intermediate scaling regime exists; in this regime the $2p_F$ susceptibility and observables such as the NMR rates $T_1$ and $T_2$ have scaling forms which we determine.

cond-mat↗

arXiv1995

Spectral Statistics Beyond Random Matrix Theory

Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the Heisenberg time. We find that the singularities (present for random matrix ensembles) are washed out in a grain with a finite conductance. The results are nonuniversal (they depend on the shape of the grain and on its conductance), though they suggest a generalization for any system with finite Heisenberg time.

cond-mat↗

arXiv1995

On the spin density wave transition in a two dimensional spin liquid

Strongly correlated two dimensional electrons are believed to form a spin liquid in some regimes of density and temperature. As the density is varied, one expects a transition from this spin liquid state to a spin density wave antiferromagnetic state. In this paper we show that it is self-consistent to assume that this transition is second order and, on this assumption, determine the critical behavior of the $2p_F$ susceptibility, the NMR rates $T_1$ and $T_2$ and the uniform susceptibility. We compare our results to data on high $T_c$ materials.

cond-mat↗

arXiv1994

Statistical Properties of Level Widths and Conductance Peaks in a Quantum Dot

We study the statistics of level widths of a quantum dot with extended contacts in the absence of time-reversal symmetry. The widths are determined by the amplitude of the wavefunction averaged over the contact area. The distribution function of level widths for a two-point contact is evaluated exactly. The distribution resembles closely the result obtained when the wavefunction fluctuates independently at each point, but differs from the one-point case. Analytical calculations and numerical simulations show that the distribution for many-point contacts has a power-law behavior at small level widths. The exponent is given by the number of points in the lead and diverges in the continuous limit. The distribution of level widths is used to determine the distribution of conductance peaks in the resonance regime. At intermediate temperatures, we find that the distribution tends to normal and fluctuations in the height of the peaks are suppressed as the lead size is increased.

cond-mat↗

arXiv1994

On the low energy properies of fermions with singular interactions

We calculate the fermion Green function and particle-hole susceptibilities for a degenerate two-dimensional fermion system with a singular gauge interaction. We show that this is a strong coupling problem, with no small parameter other than the fermion spin degeneracy, N. We consider two interactions, one arising in the context of the $t-J$ model and the other in the theory of half-filled Landau level. For the fermion self energy we show in contrast to previous claims that the qualitative behavior found in the leading order of perturbation theory is preserved to all orders in the interaction. The susceptibility $χ_Q$ at a general wavevector $\bf{Q} \neq 2\bf{p_F}$ retains the fermi-liquid form. However the $2p_F$ susceptibility $χ_{2p_F}$ either diverges as $T -> 0$ or remains finite but with nonanalytic wavevector, frequency and temperature dependence. We express our results in the language of recently discussed scaling theories, give the fixed-point action, and show that at this fixed point the fermion-gauge-field interaction is marginal in $d=2$, but irrelevant at low energies in $d \ge 2$.

cond-mat↗

arXiv1994

Non-equilibrium noise in a mesoscopic conductor: microscopic analysis

Current fluctuations are studied in a mesoscopic conductor using non-equilibrium Keldysh technique. We derive a general expression for the fluctuations in the presence of a time dependent voltage, valid for arbitrary relation between voltage and temperature. Two limits are then treated: a pulse of voltage and a DC voltage. A pulse of voltage causes phase sensitive current fluctuations for which we derive microscopically an expression periodic in $\int V(t)dt$ with the period $h/e$. Applied to current fluctuations in Josephson circuits caused by phase slips, it gives an anomalous contribution to the noise with a logarithmic singularity near the critical current. In the DC case, we get quantum to classical shot noise reduction factor 1/3, in agreement with recent results of Beenakker and Büttiker.

cond-mat↗

arXiv1994

Crossover Driven by Time-reversal Symmetry Breaking in Quantum Chaos

Parametric correlations of energy spectra of quantum chaotic systems are presented in the orthogonal-unitary and symplectic-unitary crossover region. The spectra are allowed to disperse as a function of two external perturbations: one of which preserves time-reversal symmetry, while the other violates it. Exact analytical expressions for the parametric two-point autocorrelation function of the density of states are derived in the crossover region by means of the supermatrix method. For the orthogonal-unitary crossover, the velocity distributions is determined and shown to deviate from Gaussian.

cond-mat↗

arXiv1994

Manifestation of Quantum Chaos in Electronic Band Structures

We use semiconductors as an example to show that quantum chaos manifests itself in the energy spectrum of crystals. We analyze the {\it ab initio} band structure of silicon and the tight-binding spectrum of the alloy $Al_xGa_{1-x}As$, and show that some of their statistical properties obey the universal predictions of quantum chaos derived from the theory of random matrices. Also, the Bloch momenta are interpreted as external, tunable, parameters, acting on the reduced (unit cell) Hamiltonian, in close analogy to Aharonov-Bohm fluxes threading a torus. They are used in the investigation of the parametric autocorrelator of crystal velocities. We find that our results are in good agreement with the universal curves recently proposed by Simons and coworkers.

cond-mat↗

arXiv1994

Effective lowering of the dimensionality in strongly correlated two dimensional electron gas

We study a system of fermions interacting with a gauge field which can be used to describe either spin liquid or $ν=1/2$ Quantum Hall state. We propose a generalized model with a dimensionless parameter $N$. We evaluate the properties of the model in both limits $N \gg 1$ and $N \ll 1$ and deduce the properties of the model in the most physically intersting case of $N=1,2$. At $N \ll 1$ the motion of the fermions becomes one dimensional. This allows us to obtain the fermion Green function and response functions applying bozonization method in this limit.

cond-mat↗

arXiv1994

Universal Spectral Correlations at the Mobility Edge

We demonstrate the level statistics in the vicinity of the Anderson transition in $d>2$ dimensions to be universal and drastically different from both Wigner-Dyson in the metallic regime and Poisson in the insulator regime. The variance of the number of levels $N$ in a given energy interval with $\langle N\rangle\gg1$ is proved to behave as $\langle N\rangle^γ$ where $γ=1-(νd)^{-1}$ and $ν$ is the correlation length exponent. The inequality $γ<1$, shown to be required by an exact sum rule, results from nontrivial cancellations (due to the causality and scaling requirements) in calculating the two-level correlation function.

cond-mat↗

arXiv1993

On the theory of the spin gap in bilayer cuprates

We formulate and solve a model of two planes of antiferromagnetically correlated electrons coupled together by a weak antiferromagnetic interaction of strength $λ$. We show that in-plane antiferromagnetic correlations dramatically enhance the pairing effect of the interplane interaction. For the case where the in-plane correlation length $κ^{-1} \sim T^{-1/2}$, we find that the interaction $λ$ leads to spin pairing at a temperature $T^{*} \sim λ$, much higher than the usual BCS result $exp(-J/λ)$. We suggest that this is a possible explanation of the spin gap effects observed below $T^{*} \sim 150K$ in $YBa_2Cu_3O_{6.6}$.

cond-mat↗

arXiv1993

Impurities and Quasi-One Dimensional Transport in a D-wave Superconductor

Impurity scattering in the unitary limit produces low energy quasiparticles with anisotropic spectrum in a two-dimensional $d$-wave superconductor. We describe a new {\em quasi-one-dimensional } limit of the quasiparticle scattering, which might occur in a superconductor with short coherence length and with {\em finite} impurity potential range. The dc conductivity in a $d$-wave superconductor is predicted to be proportional to the normal state scattering rate and is impurity-{\em dependent}. We show that the {\em quasi-one-dimensional } regime occurs in high-$T_c$ superconductors at low temperatures $T\lesssim 10$~K. We argue that the impurities produce weak localization, in the {\em orthogonal } universality class, of the quasiparticles in a $d$-wave superconductor.

cond-mat↗