arXiv subjects

Oded Agam

Publications and source records attributed to Oded Agam.

45 records · Page 3Linked to original sources

arXiv2000

"Quantum phase transitions" in classical nonequilibrium processes

Diffusion limited reaction of the Lotka-Volterra type is analyzed taking into account the discrete nature of the reactants. In the continuum approximation, the dynamics is dominated by an elliptic fixed-point. This fixed-point becomes unstable due to discretization effects, a scenario similar to quantum phase transitions. As a result, the long-time asymptotic behavior of the system changes and the dynamics flows into a limit cycle. The results are verified by numerical simulations.

cond-mat↗

arXiv1999

Statistics of photodissociation spectra: nonuniversal properties

We consider the two-point correlation function of the photodissociation cross section in molecules where the fragmentation process is indirect, passing through resonances above the dissociation threshold. In the limit of overlapping resonances, a formula is derived, relating this correlation function to the behavior of the corresponding classical system. It is shown that nonuniversal features of the two-point correlation function may have significant experimental manifestations.

cond-mat↗

arXiv1999

A diagrammatic approach for open chaotic systems

A semiclassical diagrammatic approach is constructed for calculating correlation functions of observables in open chaotic systems with time reversal symmetry. The results are expressed in terms of classical correlation functions involving Wigner representations of the observables. The formalism is used to explain a recent microwave experiment on the 4-disk problem, and to characterize the two-point function of the photodissociation cross section of complex molecules.

cond-mat.mes-hall↗

arXiv1999

The Accuracy of Semiclassical Quantization for Integrable Systems

The eigenvalues of the Hyperspherical billiard are calculated in the semiclassical approximation. The eigenvalues where this approximation fails are identified and found to be related to caustics that approach the wall of the billiard. The fraction of energy levels for which the semiclassical error is larger than some given value is calculated analytically (and tested numerically) and found to be independent of energy. The implications for other systems, in particular integrable ones, are discussed.

chao-dyn↗

arXiv1998

Nonequilibrium effects in the tunneling conductance spectra of small metallic particles

The tunneling spectra of small metallic grains shows an unusual structure of the differential conductance peaks. Namely, resonance peaks appear in clusters, or develop substructure as the the gate voltage is changed. These features are manifestations of a nonequilibrium behavior which appears when the applied source-drain voltage is sufficiently large. Electron-electron Coulomb interaction as well as an attractive pairing interaction play an important role in determining the magnitude and energy scales of the phenomena. For normal grains each cluster of resonances is identified with one excited single-electron state of the metal particle, shifted as a result of the different nonequilibrium occupancy configurations of the other single-electron states. For superconducting grains in the odd charging state, the substructure of the resonance is explained by nonequilibrium ``gapless'' excitations associated with different energy levels occupied by the unpaired electron. The excitations are generated by inelastic cotunneling.

cond-mat↗

arXiv1997

Nonequilibrium and Parity Effects in the Tunneling Conductance of Ultrasmall Superconducting Grains

Recent experiment on the tunneling spectra of ultrasmall superconducting grains revealed an unusual structure of the lowest differential conductance peak for grains in the odd charging states. We explain this behavior by nonequilibrium ``gapless'' excitations associated with different energy levels occupied by the unpaired electron. These excitations are generated by inelastic cotunneling.

cond-mat.mes-hall↗

arXiv1996

Chaos, interactions, and nonequilibrium effects in the tunneling resonance spectra of small metallic particles

We explain the observation of clusters in the tunneling resonance spectra of small metallic particles of few nanometer size. Each cluster of resonances is identified with one excited single--electron state of the metal particle, shifted as a result of the different nonequilibrium occupancy configurations of the other single--electron states. Assuming the underlying classical dynamics of the electrons to be chaotic, we determine the typical shift to be $Δ/g$ where $g$ is the dimensionless conductance of the grain.

cond-mat↗

arXiv1995

Approach to ergodicity in quantum wave functions

According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here develop a semiclassical theory that relates the rate of approach to the decay of certain classical fluctuations. For uniformly hyperbolic systems we find that the variance of the quantum matrix elements is proportional to the variance of the integral of the associated classical operator over trajectory segments of length $T_H$, and inversely proportional to $T_H^2$, where $T_H=h\barρ$ is the Heisenberg time, $\barρ$ being the mean density of states. Since for these systems the classical variance increases linearly with $T_H$, the variance of the matrix elements decays like $1/T_H$. For non-hyperbolic systems, like Hamiltonians with a mixed phase space and the stadium billiard, our results predict a slower decay due to sticking in marginally unstable regions. Numerical computations supporting these conclusions are presented for the bakers map and the hydrogen atom in a magnetic field.

chao-dyn↗

arXiv1995

Spectral Statistics: From Disordered to Chaotic Systems

The relation between disordered and chaotic systems is investigated. It is obtained by identifying the diffusion operator of the disordered systems with the Perron-Frobenius operator in the general case. This association enables us to extend results obtained in the diffusive regime to general chaotic systems. In particular, the two--point level density correlator and the structure factor for general chaotic systems are calculated and characterized. The behavior of the structure factor around the Heisenberg time is quantitatively described in terms of short periodic orbits.

cond-mat↗