arXiv subjects

J. W. Clark

Publications and source records attributed to J. W. Clark.

At least 55 records · Page 3Linked to original sources

arXiv2009

Interplay of single-particle and collective degrees of freedom near the quantum critical point

Competing scenarios for quantum critical points (QCPs) of strongly interacting Fermi systems signaled by a divergent density of states at zero temperature are contrasted. The conventional scenario, which enlists critical fluctuations of a collective mode and attributes the divergence to a coincident vanishing of the quasiparticle strength $z$, is shown to be incompatible with identities arising from conservation laws prevailing in the fermionic medium. An alternative scenario, in which the topology of the Fermi surface is altered at the QCP, is found to explain the non-Fermi-liquid thermodynamic behavior observed experimentally in Yb-based compounds close to the QCP. It is suggested that combination of the topological scenario with the theory of quantum phase transitions will provide a proper foundation for analysis of the extended QCP region.

cond-mat.str-el↗

arXiv2008

Statistical Global Modeling of Beta-Decay Halflives Systematics Using Multilayer Feedforward Neural Networks and Support Vector Machines

In this work, the beta-decay halflives problem is dealt as a nonlinear optimization problem, which is resolved in the statistical framework of Machine Learning (LM). Continuing past similar approaches, we have constructed sophisticated Artificial Neural Networks (ANNs) and Support Vector Regression Machines (SVMs) for each class with even-odd character in Z and N to global model the systematics of nuclei that decay 100% by the beta-minus-mode in their ground states. The arising large-scale lifetime calculations generated by both types of machines are discussed and compared with each other, with the available experimental data, with previous results obtained with neural networks, as well as with estimates coming from traditional global nuclear models. Particular attention is paid on the estimates for exotic and halo nuclei and we focus to those nuclides that are involved in the r-process nucleosynthesis. It is found that statistical models based on LM can at least match or even surpass the predictive performance of the best conventional models of beta-decay systematics and can complement the latter.

nucl-th↗

arXiv2008

Decoding Beta-Decay Systematics: A Global Statistical Model for Beta^- Halflives

Statistical modeling of nuclear data provides a novel approach to nuclear systematics complementary to established theoretical and phenomenological approaches based on quantum theory. Continuing previous studies in which global statistical modeling is pursued within the general framework of machine learning theory, we implement advances in training algorithms designed to improved generalization, in application to the problem of reproducing and predicting the halflives of nuclear ground states that decay 100% by the beta^- mode. More specifically, fully-connected, multilayer feedforward artificial neural network models are developed using the Levenberg-Marquardt optimization algorithm together with Bayesian regularization and cross-validation. The predictive performance of models emerging from extensive computer experiments is compared with that of traditional microscopic and phenomenological models as well as with the performance of other learning systems, including earlier neural network models as well as the support vector machines recently applied to the same problem. In discussing the results, emphasis is placed on predictions for nuclei that are far from the stability line, and especially those involved in the r-process nucleosynthesis. It is found that the new statistical models can match or even surpass the predictive performance of conventional models for beta-decay systematics and accordingly should provide a valuable additional tool for exploring the expanding nuclear landscape.

nucl-th↗

arXiv2008

Topology of the Fermi Surface Beyond the Quantum Critical Point

We examine the nature of phase transitions occurring in strongly correlated Fermi systems at the quantum critical point (QCP) associated with a divergent effective mass. Conventional scenarios for the QCP involving collective degrees of freedom are shown to have serious shortcomings. Working within the original Landau quasiparticle picture, we propose an alternative topological scenario for the QCP, in systems that obey standard Fermi liquid (FL) theory in advance of the QCP. Applying the technique of Poincaré mapping, we analyze the sequence of iterative maps generated by the Landau equation for the single-particle spectrum at zero temperature. It is demonstrated that the Fermi surface is subject to rearrangement beyond the QCP. If the sequence of maps converges, a multi-connected Fermi surface is formed. If it fails to converge, the Fermi surface swells into a volume that provides a measure of entropy associated with formation of an exceptional state of the system characterized by partial occupation of single-particle states and dispersion of their spectrum proportional to temperature. Based on this dual scenario, the thermodynamics of Fermi systems beyond the QCP exhibits striking departures from the predictions of standard FL theory. Mechanisms for the release of the entropy excess of the exceptional state are discussed.

cond-mat.str-el↗

arXiv2008

Non-Fermi-Liquid Behavior from the Fermi-Liquid Approach

Non-Fermi liquid behavior of strongly correlated Fermi systems is derived within the Landau approach. We attribute this behavior to a phase transition associated with a rearrangement of the Landau state that leads to flattening of a portion of the single-particle spectrum $ε({\bf p})$ in the vicinity of the Fermi surface. We demonstrate that the quasiparticle subsystem responsible for the flat spectrum possesses the same thermodynamic properties as a gas of localized spins. Theoretical results compare favorably with available experimental data. While departing radically from prevalent views on the origin of non-Fermi-liquid behavior, the theory advanced here is nevertheless a conservative one of in continuing to operate within the general framework of Landau theory.

cond-mat.str-el↗

arXiv2007

Improved Quantum Hard-Sphere Ground-State Equations of State

The London ground-state energy formula as a function of number density for a system of identical boson hard spheres, corrected for the reduced mass of a pair of particles in a sphere-of-influence picture, and generalized to fermion hard-sphere systems with two and four intrinsic degrees of freedom, has a double-pole at the ultimate \textit{regular} (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are contructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, appropriately extrapolated to intermediate densities, but whose ultimate density is irregular or \textit{random} closest close-packing as suggested in studies of a classical system of hard spheres. Results show substantially improved agreement with the best available Green-function Monte Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder, variational Fermi hypernetted chain, and so-called L-expansion data for two-component fermions.

cond-mat.stat-mech↗

arXiv2007

Properties of the Two-Dimensional Electron Gas Close to the Fermi-Liquid Quantum Critical Point

The rearrangement of single-particle degrees of freedom of a dilute two-dimensional electron gas in the vicinity of the quantum critical point is examined within a microscopic approach. It is shown that just beyond the critical point, the Landau state undergoes self-consistent rearrangement of the quasiparticle spectrum and momentum distribution. At very low temperatures, there emerges a multi-connected quasiparticle momentum distribution. With increasing temperature, two crossovers occur: a fermion condensate appears in the first and disappears in the second, giving way to universal non-Fermi-liquid behavior. Manifestations of these crossovers in thermodynamic properties of the electron gas are studied and characterized. The four quasiparticle phases predicted to exist in the vicinity of the critical point are collected in a schematic phase diagram.

cond-mat.str-el↗

arXiv2007

A Global Model of $β^-$-Decay Half-Lives Using Neural Networks

Statistical modeling of nuclear data using artificial neural networks (ANNs) and, more recently, support vector machines (SVMs), is providing novel approaches to systematics that are complementary to phenomenological and semi-microscopic theories. We present a global model of $β^-$-decay halflives of the class of nuclei that decay 100% by $β^-$ mode in their ground states. A fully-connected multilayered feed forward network has been trained using the Levenberg-Marquardt algorithm, Bayesian regularization, and cross-validation. The halflife estimates generated by the model are discussed and compared with the available experimental data, with previous results obtained with neural networks, and with estimates coming from traditional global nuclear models. Predictions of the new neural-network model are given for nuclei far from stability, with particular attention to those involved in r-process nucleosynthesis. This study demonstrates that in the framework of the $β^-$-decay problem considered here, global models based on ANNs can at least match the predictive performance of the best conventional global models rooted in nuclear theory. Accordingly, such statistical models can provide a valuable tool for further mapping of the nuclidic chart.

nucl-th↗

arXiv2007

Merging of single-particle levels and non-Fermi-liquid behavior of finite Fermi systems

We examine the problem of finite Fermi systems having a degenerate single-particle spectrum and show that the Landau approach, applied to such a system, admits the possibility of merging single-particle levels. It is demonstrated that the opportunity for this behavior is widespread in quantum many-body systems. The salient feature of the phenomenon is the occurrence of nonintegral quasiparticle occupation numbers, leading to a radical alteration of the standard quasiparticle picture. Implications of this alteration are considered for nuclear, atomic, and solid-state systems.

cond-mat.str-el↗

arXiv2006

Merging of single-particle levels in finite Fermi systems

Properties of the distribution of single-particle levels adjacent to the Fermi surface in finite Fermi systems are studied, focusing on the case in which these levels are degenerate. The interaction of the quasiparticles occupying these levels lifts the degeneracy and affects the distance between the closest levels on opposite sides of the Fermi surface, as the number of particles in the system is varied. In addition to the familiar scenario of level crossing, a new phenomenon is uncovered, in which the merging of single-particle levels results in the disappearance of well-defined single-particle excitations. Implications of this finding are discussed for nuclear, solid-state, and atomic systems.

cond-mat.str-el↗

arXiv2006

Nodes of the Gap Function and Anomalies in Thermodynamic Properties of Superfluid $^3$He

Departures of thermodynamic properties of three-dimensional superfluid $^3$He from the predictions of BCS theory are analyzed. Attention is focused on deviations of the ratios $Δ(T=0)/T_c$ and $[C_s(T_c)-C_n(T_c)]/C_n(T_c)$ from their BCS values, where $Δ(T=0)$ is the pairing gap at zero temperature, $T_c$ is the critical temperature, and $C_s$ and $C_n$ are the superfluid and normal specific heats. We attribute these deviations to the momentum dependence of the gap function $Δ(p)$, which becomes well pronounced when this function has a pair of nodes lying on either side of the Fermi surface. We demonstrate that such a situation arises if the P-wave pairing interaction $V(p_1,p_2)$, evaluated at the Fermi surface, has a sign opposite to that anticipated in BCS theory. Taking account of the momentum structure of the gap function, we derive a closed relation between the two ratios that contains no adjustable parameters and agrees with the experimental data. Some important features of the effective pairing interaction are inferred from the analysis.

cond-mat.supr-con↗

arXiv2006

Modeling Nuclear Properties with Support Vector Machines

We have made initial studies of the potential of support vector machines (SVM) for providing statistical models of nuclear systematics with demonstrable predictive power. Using SVM regression and classification procedures, we have created global models of atomic masses, beta-decay halflives, and ground-state spins and parities. These models exhibit performance in both data-fitting and prediction that is comparable to that of the best global models from nuclear phenomenology and microscopic theory, as well as the best statistical models based on multilayer feedforward neural networks.

nucl-th↗

arXiv2005

Entanglement Properties Of Quantum Many-Body Wave Functions

Entanglement properties of the trial many-body wave functions in variational treatments of the transverse Ising model in two, three, and four dimensions are investigated. Based on data for magnetizations and correlation functions generated by for symmetry-breaking Hartree-Jastrow trial ground states, results are presented for several measures of bipartite entanglement, including the von Neumann entropy of a single spin in the lattice, the concurrence between two spins, and a lower bound on the localizable entanglement, as functions of coupling strength. A simple relation is established between the Hartree-Jastrow states and the nilpotent polynomial representation of multipartite entanglement. In addition, some general comments are made on the entanglement properties of classes of many-body wave functions commonly adopted in theories of strongly correlated quantum systems.

cond-mat.stat-mech↗

arXiv2005

Nuclear mass systematics by complementing the Finite Range Droplet Model with neural networks

A neural-network model is developed to reproduce the differences between experimental nuclear mass-excess values and the theoretical values given by the Finite Range Droplet Model. The results point to the existence of subtle regularities of nuclear structure not yet contained in the best microscopic/phenomenological models of atomic masses. Combining the FRDM and the neural-network model, we create a hybrid model with improved predictive performance on nuclear-mass systematics and related quantities.

nucl-th↗

arXiv2005

One and two proton separation energies from nuclear mass systematics using neural networks

We deal with the systematics of one and two proton separation energies as predicted by our latest global model for the masses of nuclides developed with the use of neural networks. Among others, such systematics is useful as input to the astrophysical rp-process and to the one and two proton radioactive studies. Our results are compared with the experimental separation energies referred to in the 2003 Atomic Mass Evaluation and with those evaluated from theoretical models for the masses of nuclides, like the FRDM of Möller et al. and the HFB2 of Pearson et al. We focus in particular on the proton separation energies for nuclides that are involved in the rp-process (29<=Z<=40) but they have not yet been studied experimentally.

nucl-th↗

arXiv2005

Elliptical orbits in the Bloch sphere

As is well known, when an SU(2) operation acts on a two-level system, its Bloch vector rotates without change of magnitude. Considering a system composed of two two-level systems, it is proven that for a class of nonlocal interactions of the two subsystems including σ_i\otimesσ_j (with i,j \in {x,y,z}) and the Heisenberg interaction, the geometric description of the motion is particularly simple: each of the two Bloch vectors follows an elliptical orbit within the Bloch sphere. The utility of this result is demonstrated in two applications, the first of which bears on quantum control via quantum interfaces. By employing nonunitary control operations, we extend the idea of controllability to a set of points which are not necessarily connected by unitary transformations. The second application shows how the orbit of the coherence vector can be used to assess the entangling power of Heisenberg exchange interaction.

quant-ph↗

arXiv2005

Probabilistic Quantum Control Via Indirect Measurement

The most basic scenario of quantum control involves the organized manipulation of pure dynamical states of the system by means of unitary transformations. Recently, Vilela Mendes and Mank'o have shown that the conditions for controllability on the state space become less restrictive if unitary control operations may be supplemented by projective measurement. The present work builds on this idea, introducing the additional element of indirect measurement to achieve a kind of remote control. The target system that is to be remotely controlled is first entangled with another identical system, called the control system. The control system is then subjected to unitary transformations plus projective measurement. As anticipated by Schrodinger, such control via entanglement is necessarily probabilistic in nature. On the other hand, under appropriate conditions the remote-control scenario offers the special advantages of robustness against decoherence and a greater repertoire of unitary transformations. Simulations carried out for a two-level system demonstrate that, with optimization of control parameters, a substantial gain in the population of reachable states can be realized.

quant-ph↗

arXiv2005

Damping effects and the metal-insulator transition in the two-dimensional electron gas

The damping of single-particle degrees of freedom in strongly correlated two-dimensional Fermi systems is analyzed. Suppression of the scattering amplitude due to the damping effects is shown to play a key role in preserving the validity of the Landau-Migdal quasiparticle picture in a region of a phase transition, associated with the divergence of the quasiparticle effective mass. The results of the analysis are applied to elucidate the behavior of the conductivity $σ(T)$ of the two-dimensional dilute electron gas in the density region where it undergoes a metal-insulator transition.

cond-mat.str-el↗