arXiv subjects

Y. Alhassid

Publications and source records attributed to Y. Alhassid.

126 records · Page 7Linked to original sources

arXiv1998

The Spectral Autocorrelation Function in Weakly Open Chaotic Systems: Indirect Photodissociation of Molecules

We derive the statistical limit of the spectral autocorrelation function and of the survival probability for the indirect photodissociation of molecules in the regime of non-overlapping resonances. The results are derived in the framework of random matrix theory, and hold more generally for any chaotic quantum system that is weakly coupled to the continuum. The "correlation hole" that characterizes the spectral autocorrelation in the bound molecule diminishes as the typical average total width of a resonance increases.

chao-dyn↗

arXiv1998

Conductance Peak Distributions in Quantum Dots at Finite Temperature: Signatures of the Charging Energy

We derive the finite temperature conductance peak distributions and peak-to-peak correlations for quantum dots in the Coulomb blockade regime assuming the validity of random matrix theory. The distributions are universal, depending only on the symmetry class and the temperature measured in units of the mean level spacing, $Δ$. When the temperature is comparable to $Δ$ several resonances contribute to the same conductance peak and we find significant deviations from the previously known $T \ll Δ$ distributions. In contrast to the $T \ll Δ$ case, these distributions show a strong signature of the charging energy and charge quantization on the dot.

cond-mat.mes-hall↗

arXiv1998

Statistical Fluctuations of Electromagnetic Transition Intensities in pf-Shell Nuclei

We study the fluctuation properties of E2 and M1 transition intensities among T=0,1 states of A = 60 nuclei in the framework of the interacting shell model, using a realistic effective interaction for pf-shell nuclei with a Ni56 as a core. It is found that the B(E2) distributions are well described by the Gaussian orthogonal ensemble of random matrices (Porter-Thomas distribution) independently of the isobaric quantum number T_z. However, the statistics of the B(M1) transitions is sensitive to T_z: T_z=1 nuclei exhibit a Porter-Thomas distribution, while a significant deviation from the GOE statistics is observed for self-conjugate nuclei (T_z=0).

nucl-th↗

arXiv1998

Total and Parity-Projected Level Densities of Iron-Region Nuclei by the Shell Model Monte Carlo Method

Total and parity-projected level densities of iron-region nuclei are calculated microscopically by using Monte Carlo methods for the nuclear shell model in the complete $(pf+0g_{9/2})$-shell. The calculated total level density is found to be in good agreement with the experimental level density. The Monte Carlo calculations offer a significant improvement over the thermal Hartree-Fock approximation. Contrary to the Fermi gas model, it is found that the level density has a significant parity-dependence in the neutron resonance region. The systematics of the level density parameters (including shell effects) in the iron region is presented.

nucl-th↗

arXiv1997

The Perturbed Static Path Approximation at Finite Temperature: Observables and Strength Functions

We present an approximation scheme for calculating observables and strength functions of finite fermionic systems at finite temperature such as hot nuclei. The approach is formulated within the framework of the Hubbard-Stratonovich transformation and goes beyond the static path approximation and the RPA by taking into account small amplitude time-dependent fluctuations around each static value of the auxiliary fields. We show that this perturbed static path approach can be used systematically to obtain good approximations for observable expectation values and for low moments of the strength function. The approximation for the strength function itself, extracted by an analytic continuation from the imaginary-time response function, is not always reliable, and we discuss the origin of the discrepancies and possible improvements. Our results are tested in a solvable many-body model.

nucl-th↗

arXiv1997

Total and Parity-Projected Level Densities of Iron-Region Nuclei in the Auxiliary Fields Monte Carlo Shell Model

We use the auxiliary-fields Monte Carlo method for the shell model in the complete $(pf+0g_{9/2})$-shell to calculate level densities. We introduce parity projection techniques which enable us to calculate the parity dependence of the level density. Results are presented for $^{56}$Fe, where the calculated total level density is found to be in remarkable agreement with the experimental level density. The parity-projected densities are well described by a backshifted Bethe formula, but with significant dependence of the single-particle level-density and backshift parameters on parity. We compare our exact results with those of the thermal Hartree-Fock approximation.

nucl-th↗

arXiv1996

Conductance Peak Distributions in Quantum Dots and the Crossover between Orthogonal and Unitary Symmetries

Closed expressions are derived for the resonance widths and Coulomb blockade conductance peak heights in quantum dots for the crossover regime between conserved and broken time-reversal symmetry. The results hold for leads with any number of possibly correlated and inequivalent channels. Our analytic predictions are in good agreement with simulations of both random matrices and a chaotic billiard with a magnetic flux line.

cond-mat↗

arXiv1996

Signatures of Chaos in the Statistical Distribution of Conductance Peaks in Quantum Dots

Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained using random matrix theory and are valid in general for any number of non-equivalent and correlated channels, assuming that the underlying classical dynamic of the electrons in the dot is chaotic or that the dot is weakly disordered. The results are expressed in terms of the channel correlation matrix which for chaotic systems is given in closed form for both point-like contacts and extended leads. We study the dependence of the distributions on the number of channels and their correlations. The theoretical distributions are in good agreement with those computed in a dynamical model of a chaotic billiard.

cond-mat↗

arXiv1996

Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots

We show that the parametric correlations of the conductance peak amplitudes of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime become universal upon an appropriate scaling of the parameter. We compute the universal forms of this correlator for both cases of conserved and broken time reversal symmetry. For a symmetric dot the correlator is independent of the details in each lead such as the number of channels and their correlation. We derive a new scaling, which we call the rotation scaling, that can be computed directly from the dot's eigenfunction rotation rate or alternatively from the conductance peak heights, and therefore does not require knowledge of the spectrum of the dot. The relation of the rotation scaling to the level velocity scaling is discussed. The exact analytic form of the conductance peak correlator is derived at short distances. We also calculate the universal distributions of the average level width velocity for various values of the scaled parameter. The universality is illustrated in an Anderson model of a disordered dot.

cond-mat↗

arXiv1996

Universal Parametric Correlations of Conductance Peaks in Quantum Dots

We compute the parametric correlation function of the conductance peaks in chaotic and weakly disordered quantum dots in the Coulomb blockade regime and demonstrate its universality upon an appropriate scaling of the parameter. For a symmetric dot we show that this correlation function is affected by breaking time-reversal symmetry but is independent of the details of the channels in the external leads. We derive a new scaling which depends on the eigenfunctions alone and can be extracted directly from the conductance peak heights. Our results are in excellent agreement with model simulations of a disordered quantum dot.

cond-mat↗

arXiv1995

The Statistical Distributions of Level Widths and Conductance Peaks in Irregularly Shaped Quantum Dots

Analytical expressions for width and conductance peak distributions for quantum dots with multi-channel leads in the Coulomb blockade regime are presented for both limits of conserved and broken time-reversal symmetry. The results are valid for any number of non-equivalent and correlated channels, and the distributions are expressed in terms of the channel correlation matrix $M$ in each lead. The matrix $M$ is also given in closed form. A chaotic billiard is used as a model to test numerically the theoretical predictions.

cond-mat↗

arXiv1995

Shell Model Monte Carlo Studies of $γ$-Soft Nuclei

We present Shell Model Monte Carlo calculations for nuclei within the full major shell 50-82 for both protons and neutrons. The interaction is determined solely by self-consistency and odd-even mass differences. The methods are illustrated for ${}^{124}$Sn, ${}^{128}$Te and ${}^{124}$Xe. We calculate shape distributions, moments of inertia and pairing correlations as functions of temperature and angular velocity. Our calculations are the first microscopic evidence of $γ$-softness of nuclei in this region.

nucl-th↗

arXiv1995

Shell-model Monte Carlo studies of fp-shell nuclei

We study the gross properties of even-even and $N=Z$ nuclei with $A=48-64$ using shell-model Monte Carlo methods. Our calculations account for all $0 \hbar ω$ configurations in the $fp$-shell and employ the modified Kuo-Brown interaction KB3. We find good agreement with data for masses and total $B(E2)$ strengths, the latter employing effective charges $e_p=1.35e$ and $e_n=0.35e$. The calculated total Gamow-Teller strengths agree consistently with the $B(GT_+)$-values deduced from $(n,p)$ data if the shell model results are renormalized by $0.64$, as has already been established for $sd$-shell nuclei. The present calculations therefore suggest that this renormalization (i.e., $g_A=1$ in the nuclear medium) is universal.

nucl-th↗

arXiv1995

Universal Parametric Correlations of Eigenfunctions in Chaotic and Disordered Systems

This paper establishes the universality of parametric correlations of eigenfunctions in chaotic and weakly disordered systems. We demonstrate this universality in the framework of the gaussian random matrix process and obtain predictions for a number of parametric correlators, one of them analytically. We present numerical evidence from different models that verifies our predictions.

cond-mat↗

arXiv1995

Thermal properties of Fe-54

We study the thermal properties of Fe-54 with the Brown-Richter interaction in the complete 1p0f model space. Monte Carlo calculations show a peak in the heat capacity and rapid increases in both the moment of inertia and M1 strength near a temperature of 1.1 MeV that are associated with the vanishing of proton-proton and neutron-neutron monopole pair correlations; neutron-proton correlations persist to higher temperatures. Our results are consistent with a Fermi gas level density whose back-shift vanishes with increasing temperature.

nucl-th↗

arXiv1994

Complete 0 hbar omega calculations of Gamow-Teller strengths for nuclei in the iron region

Gamow-Teller strengths for selected nuclei in the iron region (A~56) have been investigated via shell-model Monte Carlo calculations with realistic interactions in the complete fp basis. Results for all cases show significant quenching relative to single-particle estimates, in quantitative agreement with (n,p) data. The J=1,T=0 residual interaction and the f_{7/2}-f_{5/2} spin-orbit splitting are shown to play major roles in the quenching mechanism. Calculated B(E2, 2^+_1 -> 0^+_1) values are in fair agreement with experiment using effective charges of e_p=1.1e and e_n=0.1e.

nucl-th↗

arXiv1993

Practical solution to the Monte Carlo sign problem: Realistic calculations of 54Fe

We present a practical solution to the "sign problem" in the auxiliary field Monte Carlo approach to the nuclear shell model. The method is based on extrapolation from a continuous family of problem-free Hamiltonians. To demonstrate the resultant ability to treat large shell-model problems, we present results for 54Fe in the full fp-shell basis using the Brown-Richter interaction. We find the Gamow-Teller beta^+ strength to be quenched by 58% relative to the single-particle estimate, in better agreement with experiment than previous estimates based on truncated bases.

nucl-th↗

arXiv1993

Deformed Gaussian Orthogonal Ensemble Analysis of the Interacting Boson Model

A Deformed Gaussian Orthogonal Ensemble (DGOE) which interpolates between the Gaussian Orthogonal Ensemble and a Poissonian Ensemble is constructed. This new ensemble is then applied to the analysis of the chaotic properties of the low lying collective states of nuclei described by the Interacting Boson Model (IBM). This model undergoes a transition order-chaos-order from the $SU(3)$ limit to the $O(6)$ limit. Our analysis shows that the quantum fluctuations of the IBM Hamiltonian, both of the spectrum and the eigenvectors, follow the expected behaviour predicted by the DGOE when one goes from one limit to the other.

nucl-th↗