arXiv subjects

E. Eisenberg

Publications and source records attributed to E. Eisenberg.

At least 19 recordsLinked to original sources

arXiv2026

Pulsar timing arrays: the emerging gravitational-wave landscape

Pulsar Timing Array (PTA) experiments have entered a new era with evidence for a nanoHertz gravitational wave background (GWB). This review describes the physics of detection, detailing the noise models and cross-correlation techniques required to isolate the Hellings-Downs curve. We discuss astrophysical implications, arguing that the perceived tension between current amplitudes and standard merger models is largely resolved by new insights into supermassive black hole binary populations. Beyond the stochastic background, we review the framework for multi-messenger continuous gravitational-wave searches, highlighting targeted search campaigns and rigorous detection protocols. We also examine the potential to probe New Physics, including cosmic strings and ultralight dark matter. Critical challenges are addressed, including small-scale leakage bias in anisotropy searches and the separation of deterministic signals from the GWB and pulsar noise. Finally, we outline the field's future, from rapid data combination strategies to the sensitivity gains expected from the Square Kilometre Array Observatory (SKAO) and DSA-2000.

astro-ph.HE↗

arXiv2011

Jamming, relaxation and crystallization of a super-cooled fluid in a three-dimensional lattice

Off-equilibrium dynamics of a three-dimensional lattice model with nearest- and next nearest-neighbors exclusions is studied. At equilibrium, the model undergoes a first-order fluid-solid transition. Non-equilibrium filling, through random sequential adsorption with diffusion, creates amorphous structures and terminates at a disordered state with random closest packing density that lies in the equilibrium solid regime. The approach towards random closest packing is characterized by two distinct power-law regimes, reflecting the formation of small densely packed grains in the long time regime of the filling process. We then study the fixed-density relaxation of these amorphous structures towards the solid phase. The route to crystallization is shown to deviate from the simple grain growth proposed by classical nucleation theory. Our measurements suggest that relaxation is driven mainly by coalescence of neighboring crystallized grains which exist in the initial amorphous state.

cond-mat.stat-mech↗

arXiv2009

Ideal glass transition in a simple 2D lattice model

We present a simple lattice model showing a glassy behavior. $R$ matrix analysis predicts critical termination of the super-cooled fluid branch at density $ρ_g=0.1717$. This prediction is confirmed by dynamical numerical simulations, showing power-law divergences of relaxation time $τ_{1/2}$, as well as the 4-susceptibility $χ_4$ peak's location and height exactly at the predicted density. The power-law divergence of $χ_4$ continues up to $χ_4$ as high as $10^4$. Finite-size scaling study reveals divergence of correlation length accompanying the transition.

cond-mat.stat-mech↗

arXiv2009

Critical exponents from cluster coefficients

For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix $R_{mn}$, whose elements converge to two constants. This allows for an effective extrapolation of the equation of state for these models. Due to a nearby (nonphysical) singularity on the negative real z axis, standard methods (e.g. Padè approximants based on the cluster integrals expansion) fail to capture the behavior of these models near the ordering transition, and, in particular, do not detect the critical point. A recent work (Eisenberg and Baram, PNAS {\bf 104}, 5755 (2007)) has shown that the critical exponents $σ$ and $σ'$, characterizing the singularity of the density as a function of the activity, can be exactly calculated if the decay of the $R$ matrix elements to their asymptotic constant follows a $1/n^2$ law. Here we employ renormalization arguments to extend this result and analyze cases for which the asymptotic approach of the $R$ matrix elements towards their limiting value is of a more general form. The relevant asymptotic correction terms (in RG sense) are identified and we then provide a corrected exact formula for the critical exponents. We identify the limits of usage of the formula, and demonstrate one physical model which is beyond its range of validity. The new formula is validated numerically and then applied to analyze a number of concrete physical models.

cond-mat.stat-mech↗

arXiv2005

Dephasing Time in a Two-Dimensional Electron Fermi Liquid

The observation of coherent quantum transport phenomena in metals and semiconductors is limited by the eventual loss of phase coherence of the conducting electrons. We use the weak localization effect to measure the low-temperature dephasing time in a two-dimensional electron Fermi liquid in GaAs/AlGaAs heterostructures. We use a novel temperature calibration method based on the integer quantum Hall effect in order to directly measure the electrons' temperature. The data are in excellent agreement with recent theoretical results, including contributions from the triplet channel, for a broad temperature range. We see no evidence for saturation of the dephasing time down to around 100mK. Moreover, the zero-temperature dephasing time is extrapolated to be higher than 4ns.

cond-mat.mes-hall↗

arXiv2005

A first-order phase-transition, a super-cooled fluid, and a glass in a two-dimensional lattice gas model

Studying the series expansion of the thermodynamic potential for the hard-core N3 lattice-gas model, we provide evidence for a first-order phase-transition with a finite jump in density and entropy, in agreement with numerical transfer matrix calculations. The solid branch terminates at the transition, while the fluid branch continues beyond the critical activity, describing a meta-stable super-cooled fluid. It terminates with density 0.85 (relative to the closest packing density) and finite entropy per site. This termination density is close to the random-closest-packing density of the glassy state obtained for infinitely-fast cooling. The model thus exhibits a thermodynamic meta-stable glassy phase with finite Edwards' compactivity.

cond-mat.stat-mech↗

arXiv2003

Random matrix theory for closed quantum dots with weak spin-orbit coupling

To lowest order in the coupling strength, the spin-orbit coupling in quantum dots results in a spin-dependent Aharonov-Bohm flux. This flux decouples the spin-up and -down random matrix theory ensembles of the quantum dot. We employ this ensemble and find significant changes in the distribution of the Coulomb blockade peak height, in particular a decrease of the width of the distribution. The puzzling disagreement between standard random matrix theory and the experimental distributions by Patel et al. might possibly be attributed to these spin-orbit effects.

cond-mat.mes-hall↗

arXiv2003

The persistence length of two dimensional self avoiding random walks

The decay of directional correlations in self-avoiding random walks on the square lattice is investigated. Analysis of exact enumerations and Monte Carlo data suggest that the correlation between the directions of the first step and the j-th step of the walk decays faster than 1/j, indicating that the persistence length of the walk is finite.

cond-mat.stat-mech↗

arXiv2002

Spectral fluctuations effects on conductance peak height statistics in quantum dots

Within random matrix theory for quantum dots, both the dot's one-particle eigenlevels and the dot-lead couplings are statistically distributed. While the effect of the latter on the conductance is obvious and has been taken into account in the literature, the statistical distribution of the one-particle eigenlevels is generally replaced by a picket-fence spectrum. Here we take the random matrix theory eigenlevel distribution explicitly into account and observe significant deviations in the conductance distribution and magnetoconductance of closed quantum dots at experimentally relevant temperatures.

cond-mat.mes-hall↗

arXiv2002

The breakdown of the Nagaoka phase in the 2D t-J model

In the limit of weak exchange, J, at low hole concentration, the ground state of the 2D t-J model is believed to be ferromagnetic. We study the leading instability of this Nagaoka state, which emerges with increasing J. Both exact diagonalization of small clusters, and a semiclassical analytical calculation of larger systems show that above a certain critical value of the exchange, Nagaoka's state is unstable to phase separation. In a finite-size system a bubble of antiferromagnetic Mott insulator appears in the ground state above this threshold. The size of this bubble depends on the hole concentration and scales as a power of the system size, N.

cond-mat.str-el↗

arXiv2001

Coherent electron transport in a Si quantum dot dimer

We show that the coherence of charge transfer through a weakly coupled double-dot dimer can be determined by analyzing the statistics of the conductance pattern, and does not require large phase coherence length in the host material. We present an experimental study of the charge transport through a small Si nanostructure, which contains two quantum dots. The transport through the dimer is shown to be coherent. At the same time, one of the dots is strongly coupled to the leads, and the overall transport is dominated by inelastic co-tunneling processes.

cond-mat.mes-hall↗

arXiv1999

Glass Transition in a 2D Lattice Model

The dynamics of compaction of hard cross-shaped pentamers on the 2D square lattice is investigated. The addition of new particles is controlled by diffusive relaxation. It is shown that the filling process terminates at a glassy phase with a limiting coverage density ρ_{rcp}=0.171626(3), lower than the density of closest packing ρ_{cp}=0.2, and the long time filling rate vanishes like (ρ_{rcp}-ρ(t))^2. For the entire density regime the particles form an amorphous phase, devoid of any crystalline order. Therefore, the model supports a stable random packing state, as opposed to the hard disks system. Our results may be relevant to recent experiments studying the clustering of proteins on bilayer lipid membranes.

cond-mat.stat-mech↗

arXiv1999

Disorder Induced Ferromagnetism in Restricted Geometries

We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite $U$ Hubbard model. We find that for one dimensional systems disorder has no influence, while for two dimensional systems disorder enhances the spin polarization of the system. The tendency of disorder to enhance magnetism in the ground state may be relevant to recent experimental observations of spin polarized ground states in quantum dots and small metallic grains.

cond-mat.mes-hall↗

arXiv1999

Ground State Spin Structure of Strongly Interacting Disordered 1D Hubbard Model

We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite U 1D Hubbard model. We find that the ground state is not ferromagnetic. This is analyzed in terms of the algebraic structure of the spin dependence of the Hamiltonian. A simple explanation is derived for the 1/N periodicity in the persistent current for this model.

cond-mat.mes-hall↗

arXiv1998

Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space

We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips $S$-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the Lax-Phillips $S$-matrix is unitarily related to the $S$-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable $σ$ of the Lax-Phillips theory. Analytic continuation in $σ$ has some of the properties of a method developed some time ago for application to dilation analytic potentials. We work out an illustrative example using a Lee-Friedrichs model for the underlying dynamical system.

hep-th↗

arXiv1996

A New Time-Scale for Tunneling

We study the tunneling through an oscillating delta barrier. Using time periodicity of the model, the time-dependent Schrödinger equation is reduced to a simple but infinite matrix equation. Employing Toeplitz matrices methods, the infinite matrix is replaces by a $3\times 3$ matrix, allowing an analytical solution. Looking at the frequency dependence of the transmissionamplitudes, one observes a new time scale which dominates the tunneling dynamics. This time scale differs from the one previously introduced by Büttiker and Landauer. The relation between these two is discussed.

quant-ph↗

arXiv1996

Lax-Phillips Theory and Quantum Evolution

The scattering theory of Lax and Phillips, designed primarily for hyperbolic systems, such as electromagnetic or acoustic waves, is described. This theory provides a realization of the theorem of Foias and Nagy; there is a subspace of the Hilbert space in which the unitary evolution of the system, restricted to this subspace, is realized as a semigroup. The embedding of the quantum theory into this structure, carried out by Flesia and Piron, is reviewed. We show how the density matrix for an effectively pure state can evolve to an effectively mixed state (decoherence) in this framework. Necessary conditions are given for the realization of the relation between the spectrum of the generator of the semigroup and the singularities of the $S$-matrix (in energy representation). It is shown that these conditions may be met in the Liouville space formulation of quantum evolution, and in the Hilbert space of relativistic quantum theory.

quant-ph↗

arXiv1996

Antiresonance and Localization in Quantum Dynamics

The phenomenon of quantum antiresonance (QAR), i.e., exactly periodic recurrences in quantum dynamics, is studied in a large class of nonintegrable systems, the modulated kicked rotors (MKRs). It is shown that asymptotic exponential localization generally occurs for $η$ (a scaled $\hbar$) in the infinitesimal vicinity of QAR points $η_0$. The localization length $ξ_0$ is determined from the analytical properties of the kicking potential. This ``QAR-localization" is associated in some cases with an integrable limit of the corresponding classical systems. The MKR dynamical problem is mapped into pseudorandom tight-binding models, exhibiting dynamical localization (DL). By considering exactly-solvable cases, numerical evidence is given that QAR-localization is an excellent approximation to DL sufficiently close to QAR. The transition from QAR-localization to DL in a semiclassical regime, as $η$ is varied, is studied. It is shown that this transition takes place via a gradual reduction of the influence of the analyticity of the potential on the analyticity of the eigenstates, as the level of chaos is increased.

cond-mat↗