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Marvin Weinstein

Publications and source records attributed to Marvin Weinstein.

At least 19 recordsLinked to original sources
arXiv2014

Detection of Nuclear Sources in Search Applications using Dynamic Quantum Clustering of Spectral Data

In a search scenario, nuclear background spectra are continuously measured in short acquisition intervals with a mobile detector-spectrometer. Detecting sources from measured data is difficult because of low signal to noise ratio (S/N) of spectra, large and highly varying background due to naturally occurring radioactive material (NORM), and line broadening due to limited spectral resolution of nuclear detector. We have invented a method for detection of sources using clustering of spectral data. Our method takes advantage of the physical fact that a source not only produces counts in the region of its spectral emission, but also has the effect on the entire detector spectrum via Compton continuum. This allows characterizing the low S/N spectrum without distinct isotopic lines using multiple data features. We have shown that noisy spectra with low S/N can be grouped by overall spectral shape similarity using a data clustering technique called Dynamic Quantum Clustering (DQC). The spectra in the same cluster can then be averaged to enhance S/N of the isotopic spectral line. This would allow for increased accuracy of isotopic identification and lower false alarm rate. Our method was validated in a proof-of principle study using a data set of spectra measured in one-second intervals with Sodium Iodide detector. The data set consisted of over 7000 spectra obtained in urban background measurements, and approximately 70 measurements of Cs-137 and Co-60 sources. Using DQC analysis, we have observed that all spectra containing Cs-137 and Co-60 signal cluster away from the background.

physics.data-an↗
arXiv2012

p6 - Chiral Resonating Valence Bonds in the Kagome Antiferromagnet

The Kagome Heisenberg antiferromagnet is mapped onto an effective Hamiltonian on the star superlattice by Contractor Renormalization. Comparison of ground state energies on large lattices to Density Matrix Renormalization Group justifies truncation of effective interactions at range 3. Within our accuracy, magnetic and translational symmetries are not broken (i.e. a spin liquid ground state). However, we discover doublet spectral degeneracies which signal the onset of p6 - chirality symmetry breaking. This is understood by simple mean field analysis. Experimentally, the p6 chiral order parameter should split the optical phonons degeneracy near the zone center. Addition of weak next to nearest neighbor coupling is discussed.

cond-mat.str-el↗
arXiv2011

Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, {\em without restricting to variational ansatzes}. The lattice of size $N$ is partitioned into two subclusters. At each iteration the Lanczos vector is projected into two sets of $n_{\rm svd}$ smaller subcluster vectors using singular value decomposition. For low entanglement entropy $S_{ee}$, (satisfied by short range Hamiltonians), the truncation error is expected to vanish as $\exp(-n_{\rm svd}^{1/S_{ee}})$. Convergence is tested for the Heisenberg model on Kagomé clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given.

cond-mat.str-el↗
arXiv2011

A Different Look at Dark Energy and the Time Variation of Fundamental Constants

This paper makes the simple observation that a fundamental length, or cutoff, in the context of Friedmann-Lemaître-Robertson-Walker (FRW) cosmology implies very different things than for a static universe. It is argued that it is reasonable to assume that this cutoff is implemented by fixing the number of quantum degrees of freedom per co-moving volume (as opposed to a Planck volume) and the relationship of the vacuum-energy of all of the fields in the theory to the cosmological constant (or dark energy) is re-examined. The restrictions that need to be satisfied by a generic theory to avoid conflicts with current experiments are discussed, and it is shown that in any theory satisfying these constraints knowing the difference between $w$ and minus one allows one to predict $\dot{w}$. It is argued that this is a robust result and if this prediction fails the idea of a fundamental cutoff of the type being discussed can be ruled out. Finally, it is observed that, within the context of a specific theory, a co-moving cutoff implies a predictable time variation of fundamental constants. This is accompanied by a general discussion of why this is so, what are the strongest phenomenological limits upon this predicted variation, and which limits are in tension with the idea of a co-moving cutoff. It is pointed out, however, that a careful comparison of the predicted time variation of fundamental constants is not possible without restricting to a particular model field-theory and that is not done in this paper.

astro-ph.CO↗
arXiv2009

Strange Bedfellows: Quantum Mechanics and Data Mining

Last year, in 2008, I gave a talk titled {\it Quantum Calisthenics}. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.

cs.LG↗
arXiv2009

Dynamic quantum clustering: a method for visual exploration of structures in data

A given set of data-points in some feature space may be associated with a Schrodinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schrodinger equation. Moreover, we approximate this Hamiltonian formalism by a truncated calculation within a set of Gaussian wave functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition or feature filtering.

physics.data-an↗
arXiv2009

Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations

It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I refer to this method as a guided numerical approximation scheme and it is based upon a new look at what the path integral tells us about states in Hilbert space. I begin with simple exactly solvable models and show how to handle problems which cannot be dealt with analytically, this includes the treatment of the evolution of a Gaussian wave-packet in an anharmonic potential as well tunneling problems (i.e., instanton effects)

quant-ph↗
arXiv2008

Bootstrap Approximations in Contractor Renormalization

We propose a bootstrap method for approximating the long-range terms in the Contractor Renormalization (CORE) method. The idea is tested on the 2-D Heisenberg antiferromagnet and the frustrated J_2-J_1 model. We obtain renormalization group flows that directly reveal the Neel phase of the unfrustrated HAF and the existence of a phase transition in the J_2-J_1 model for weak frustration. However, we find that this bootstrap method is dependent on blocking and truncation schemes. For this reason, we discuss these dependencies and unresolved issues that researchers who use this approach must consider.

cond-mat.str-el↗
arXiv2007

Exploring Contractor Renormalization: Tests on the 2-D Heisenberg Antiferromagnet and Some New Perspectives

Contractor Renormalization (CORE) is a numerical renormalization method for Hamiltonian systems that has found applications in particle and condensed matter physics. There have been few studies, however, on further understanding of what exactly it does and its convergence properties. The current work has two main objectives. First, we wish to investigate the convergence of the cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This is important because the linked cluster expansion used to evaluate this formula non-perturbatively is not controlled by a small parameter. Here we present a study of three different blocking schemes which reveals some surprises and in particular, leads us to suggest a scheme for defining successive terms in the cluster expansion. Our second goal is to present some new perspectives on CORE in light of recent developments to make it accessible to more researchers, including those in Quantum Information Science. We make some comparison to entanglement-based approaches and discuss how it may be possible to improve or generalize the method.

cond-mat.str-el↗
arXiv2006

Adaptive Perturbation Theory I: Quantum Mechanics

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, $H$, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. This paper introduces the method in the context of the pure anharmonic oscillator and then goes on to apply it to the case of tunneling between both symmetric and asymmetric minima. It concludes with an introduction to the extension of these methods to the discussion of a quantum field theory. A more complete discussion of this issue will be given in the second paper in this series. This paper will show how to use the method of adaptive perturbation theory to non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.

hep-th↗
arXiv2006

Adaptive Perturbation Theory: Quantum Mechanics and Field Theory

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, $H$, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. In this talk I will introduce the method in the context of the pure anharmonic oscillator and then apply it to the case of tunneling between symmetric minima. After that, I will show how this method can be applied to field theory. In that discussion I will show how one can non-perturbatively extract the structure of mass, wavefunction and coupling constant

hep-th↗
arXiv2004

CORE: Frustrated Magnets, Charge Fractionalization and QCD

I explain how to use a simple method to extract the physics of lattice Hamiltonian systems which are not easily analyzed by exact or other numerical methods. I will then use this method to establish the relationship between QCD and a special class of generalized, highly frustrated anti-ferromagnets.

hep-th↗
arXiv2004

Cosmology Quantized in Cosmic Time

This paper discusses the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology. We show how, after a simple change of variables, to quantize the problem in a way which parallels the classical discussion. The result is that two of the Einstein equations arise as exact equations of motion and one of the usual Einstein equations (suitably quantized) survives as a constraint equation to be imposed on the space of physical states. However, the Friedmann equation, which is also a constraint equation and which is the basis of the Wheeler-deWitt equation, acquires a welcome quantum correction that becomes significant for small scale factors. To clarify the general formalism and explicitly show why we choose to weaken the statement of the Wheeler-deWitt equation, we apply the general formalism to de Sitter space. After exactly solving the relevant Heisenberg equations of motion we give a detailed discussion of the subtleties associated with defining physical states and the emergence of the classical theory. This computation provides the striking result that quantum corrections to this long wavelength limit of gravity eliminate the problem of the {\it big crunch}. We also show that the same corrections lead to possibly measurable effects on the CMB radiation. For the sake of completeness, we discuss the special case, $Λ=0$, and its relation to Minkowski space. Finally, we suggest interesting ways in which these techniques can be generalized to cast light on the question of chaotic or eternal inflation. In particular, we suggest one can put an experimental lower bound on the distance to a universe with a scale factor very different from our own, by looking at its effects on our CMB radiation.

hep-th↗
arXiv2004

Quantized Cosmology II: de Sitter Space

This work applies the formalism developed in our earlier paper to de Sitter space. After exactly solving the relevant Heisenberg equations of motion we give a detailed discussion of the subtleties associated with defining physical states and the emergence of the classical theory. This computation provides the striking result that quantum corrections to this long wavelength limit of gravity eliminate the problem of the big crunch. We also show that the same corrections lead to possibly measureable effects on the CMB radiation. Finally, for the sake of completeness we discuss the special case, $Λ=0$, and its relation to Minkowski space.

hep-th↗
arXiv2003

Quantized Cosmology

This paper discusses the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology. We show how, after a simple change of variables, one can quantize the problem in a way which parallels the classical discussion. The result is that two of the Einstein equations arise as exact equations of motion and one of the usual Einstein equations (suitably quantized) survives as a constraint equation to be imposed on the space of physical states. However, the Friedmann equation, which is also a constraint equation and which is the basis of the Wheeler-DeWitt equation, acquires a welcome quantum correction that becomes significant for small scale factors. We discuss the extension of this result to a full quantum mechanical derivation of the anisotropy ($δρ/ρ$) in the cosmic microwave background radiation, and the possibility that the extra term in the Friedmann equation could have observable consequences. Finally, we suggest interesting ways in which these techniques can be generalized to cast light on the question of chaotic or eternal inflation. In particular, we suggest one can put an experimental lower bound on the distance to a universe with a scale factor very different from our own, by looking at its effects on our CMB radiation.

hep-th↗
arXiv2002

Black Holes, Hawking Radiation and the Information Paradox

This talk is about results obtained by Kirill Melnikov and myself pertaining to the canonical quantization of a massless scalar field in the presence of a Schwarzschild black hole. After a brief summary of what we did and how we reproduce the familiar Hawking temperature and energy flux, I focus attention on how our discussion differs from other treatments. In particular I show that we can define a system which fakes an equilibrium thermodynamic object whose entropy is given by the $A/4$ (where $A$ is the area of the black hole horizon), but for which the assignment of a classical entropy to the system is incorrect. Finally I briefly discuss a discretized version of the theory which seems to indicate that things work in a surprising way near $r=0$.

hep-th↗
arXiv2002

On Unitary Evolution of a Massless Scalar Field In A Schwarzschild Background: Hawking Radiation and the Information Paradox

We develop a Hamiltonian formalism which can be used to discuss the physics of a massless scalar field in a gravitational background of a Schwarzschild black hole. Using this formalism we show that the time evolution of the system is unitary and yet all known results such as the existence of Hawking radiation can be readily understood. We then point out that the Hamiltonian formalism leads to interesting observations about black hole entropy and the information paradox.

hep-th↗