arXiv subjects

Lev Kaplan

Publications and source records attributed to Lev Kaplan.

27 records · Page 2Linked to original sources

arXiv2009

A Method to Modify RMT using Short-Time Behavior in Chaotic Systems

We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead requiring only a knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard Random Matrix Theory and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave function autocorrelations and cross-correlations, and show how the approach leads to a significant improvement in accuracy for simple chaotic systems where comparison can be made with brute-force diagonalization.

nlin.CD↗

arXiv2008

Maximal Success Probabilities of Linear-Optical Quantum Gates

Numerical optimization is used to design linear-optical devices that implement a desired quantum gate with perfect fidelity, while maximizing the success rate. For the 2-qubit CS (or CNOT) gate, we provide numerical evidence that the maximum success rate is $S=2/27$ using two unentangled ancilla resources; interestingly, additional ancilla resources do not increase the success rate. For the 3-qubit Toffoli gate, we show that perfect fidelity is obtained with only three unentangled ancilla photons -- less than in any existing scheme -- with a maximum $S=0.00340$. This compares well with $S=(2/27)^2/2 \approx 0.00274$, obtainable by combining two CNOT gates and a passive quantum filter [PRA 68, 064303 (2003)]. The general optimization approach can easily be applied to other areas of interest, such as quantum error correction, cryptography, and metrology [arXiv:0807.4906, PRL 99 070801 (2007)].

quant-ph↗

arXiv2007

Inflationary dynamics for matrix eigenvalue problems

Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the acoustic modes of a concert hall, or hundreds of other physical quantities. Often only the few eigenpairs with the lowest or highest frequency (extremal solutions) are needed. Methods that have been developed over the past 60 years to solve such problems include the Lanczos [1,2] algorithm, Jacobi-Davidson techniques [3], and the conjugate gradient method [4]. Here we present a way to solve the extremal eigenvalue/eigenvector problem, turning it into a nonlinear classical mechanical system with a modified Lagrangian constraint. The constraint induces exponential inflationary growth of the desired extremal solutions.

quant-ph↗

arXiv2002

Statistics of branched flow in a weak correlated random potential

Recent images of electron flow through a two-dimensional electron gas (2DEG) device show branching behavior that is reproduced in numerical simulations of motion in a correlated random potential [cond-mat/0010348]. We show how such branching naturally arises from caustics in the classical flow and find a simple scaling behavior of the branching under variation of the random potential strength. Analytic results describing the statistical properties of the branching are confirmed by classical and quantum numerical tests.

nlin.CD↗

arXiv2002

Odd-even binding effect from random two-body interactions

Systematic odd-even binding energy differences in finite metallic particles are usually attributed to mean-field orbital energy effects or to a coherent pairing interaction. We show analytically and numerically that a purely random two-body Hamiltonian can also give rise to an odd-even staggering. We explore the characteristics of this chaotic mechanism and discuss distinguishing features with respect to the other causes of staggering. In particular, randomness-induced staggering is found to be a smooth function of particle number, and the mechanism is seen to be largely insensitive to the presence of a magnetic field.

cond-mat.mes-hall↗

arXiv2000

Spin Structure of Many-Body Systems with Two-Body Random Interactions

We investigate the spin structure of many-fermion systems with a spin-conserving two-body random interaction. We find a strong dominance of spin-0 ground states and considerable correlations between energies and wave functions of low-lying states with different spin, but no indication of pairing. The spectral densities exhibit spin-dependent shapes and widths, and depend on the relative strengths of the spin-0 and spin-1 couplings in the two-body random matrix. The spin structure of low-lying states can largely be explained analytically.

nucl-th↗

arXiv1999

Wave Function Structure in Two-Body Random Matrix Ensembles

We study the structure of eigenstates in two-body interaction random matrix ensembles and find significant deviations from random matrix theory expectations. The deviations are most prominent in the tails of the spectral density and indicate localization of the eigenstates in Fock space. Using ideas related to scar theory we derive an analytical formula that relates fluctuations in wave function intensities to fluctuations of the two-body interaction matrix elements. Numerical results for many-body fermion systems agree well with the theoretical predictions.

nucl-th↗

arXiv1995

Effects of Top Compositeness

We investigate the effects of top quark compositeness on various physical parameters, and obtain lower limits on the compositeness scale from electroweak precision data. We consider corrections to top quark decay rates and other physical processes. Our results depend sensitively on whether the left-handed top is composite. A considerable enhancement of $t \bar t$ production is possible if only the right-handed top is composite.

hep-ph↗

arXiv1994

Decays of $\ell=1$ Baryons --- Quark Model versus Large-$N_c$

We study nonleptonic decays of the orbitally excited, \su6 \rep{70}-plet baryons in order to test the hypothesis that the successes of the nonrelativistic quark model have a natural explanation in the large-$N_c$ limit of QCD. By working in a Hartree approximation, we isolate a specific set of operators that contribute to the observed s- and d-wave decays in leading order in $1/N_c$. We fit our results to the current experimental decay data, and make predictions for a number of allowed but unobserved modes. Our tentative conclusion is that there is more to the nonrelativistic quark model of baryons than large-$N_c$.

hep-ph↗