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Sep 22, 2013
09/13

by
Mark Srednicki

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We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, and Schack, but our approach and emphasis are different. We also discuss the problem of choosing a noninformative prior for a density matrix.

Source: http://arxiv.org/abs/quant-ph/0501009v2

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Sep 23, 2013
09/13

by
Mark Srednicki

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We show that the results of Prigodin et al can be reproduced and simplified by making use of Berry's conjecture that the energy eigenfunctions in a quantized chaotic system are gaussian random variables.

Source: http://arxiv.org/abs/cond-mat/9512115v1

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Jul 20, 2013
07/13

by
Mark Srednicki

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At short distances, energy eigenfunctions of chaotic systems have spatial correlations that are well described by assuming a microcanonical density in phase space for the corresponding Wigner function. However, this is not correct on large scales. The correct correlation function is in turn needed to get the correct formula for the root-mean-square value of the off-diagonal matrix elements of simple observables, and for the fluctuations in the diagonal elements.

Source: http://arxiv.org/abs/chao-dyn/9712008v1

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Sep 22, 2013
09/13

by
Mark Srednicki

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The fluctuations in the cosmic microwave background radiation may contain deviations from gaussian statistics which would be reflected in a nonzero value of three-point correlation function of $\Delta T$. However, any potential observation of the three-point function is limited by cosmic variance, even if a whole-sky map of $\Delta T$ is available. Here I derive a general formula for the cosmic variance of the three-point function in terms of integrals over the two-point function. This formula...

Source: http://arxiv.org/abs/astro-ph/9306012v2

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Sep 22, 2013
09/13

by
Mark Srednicki

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This is a draft version of Part II of a three-part textbook on quantum field theory.

Source: http://arxiv.org/abs/hep-th/0409036v1

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Sep 18, 2013
09/13

by
Mark Srednicki

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I give a pedagogical and historical introduction to axion physics, and briefly review the present status of axions in our understanding of particle physics and cosmology. This is a contribution to Continuous Advances in QCD 2002/Arkadyfest, held in honor of Arkady Vainshtein's 60th birthday.

Source: http://arxiv.org/abs/hep-th/0210172v1

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Sep 18, 2013
09/13

by
Mark Srednicki

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We consider many-body quantum systems that exhibit quantum chaos, in the sense that the observables of interest act on energy eigenstates like banded random matrices. We study the time-dependent expectation values of these observables, assuming that the system is in a definite (but arbitrary) pure quantum state. We induce a probability distribution for the expectation values by treating the zero of time as a uniformly distributed random variable. We show explicitly that if an observable has a...

Source: http://arxiv.org/abs/cond-mat/9809360v2

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Sep 22, 2013
09/13

by
Mark Srednicki

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This is a draft version of Part I of a three-part textbook on quantum field theory.

Source: http://arxiv.org/abs/hep-th/0409035v1

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Sep 22, 2013
09/13

by
Mark Srednicki

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Matsumoto and Yoshimura [hep-ph/9910393] have argued that there are loop corrections to the number density of heavy particles (in thermal equilibrium with a gas of light particles) that are not Boltzmann suppressed by a factor of e^(-M/T) at temperatures T well below the mass M of the heavy particle. We argue, however, that their definition of the number density does not correspond to a quantity that could be measured in a realistic experiment. We consider a model where the heavy particles...

Source: http://arxiv.org/abs/hep-ph/0001090v2

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Sep 21, 2013
09/13

by
Mark Srednicki

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We show that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey {\it Berry's conjecture}. Berry's conjecture is expected to hold only if the corresponding classical system is chaotic, and essentially states that the energy eigenfunctions behave as if they were gaussian random variables. We review the existing evidence, and show that previously neglected...

Source: http://arxiv.org/abs/cond-mat/9403051v2

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Sep 21, 2013
09/13

by
Mark Srednicki

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The local Riemann hypothesis states that the zeros of the Mellin transform of a harmonic-oscillator eigenfunction (on a real or p-adic configuration space) have real part 1/2. For the real case, we show that the imaginary parts of these zeros are the eigenvalues of the Berry-Keating hamiltonian H=(xp+px)/2 projected onto the subspace of oscillator eigenfunctions of lower level. This gives a spectral proof of the local Riemann hypothesis for the reals, in the spirit of the Hilbert-Polya...

Source: http://arxiv.org/abs/1104.1850v3

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Sep 18, 2013
09/13

by
Mark Srednicki

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We show that the condition for the appearance of quantum chaos (Wigner-Dyson distribution of energy eigenvalues, gaussian-random energy eigenfunctions) in a dilute gas of many hard spheres is $\lambda \ll \ell$, where $\lambda$ is the wavelength of a typical particle and $\ell$ is the mean free path between collisions. For fermions with Fermi wavelength $\lambda_F \ll \ell$, this implies that all energy eigenstates, including the ground state, are chaotic. Physical implications are discussed.

Source: http://arxiv.org/abs/cond-mat/9605127v1

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Sep 23, 2013
09/13

by
Mark Srednicki

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We consider a quantum system with $N$ degrees of freedom which is classically chaotic. When $N$ is large, and both $\hbar$ and the quantum energy uncertainty $\Delta E$ are small, quantum chaos theory can be used to demonstrate the following results: (1) given a generic observable $A$, the infinite time average $\overline A$ of the quantum expectation value $ $ is independent of all aspects of the initial state other than the total energy, and equal to an appropriate thermal average of $A$; (2)...

Source: http://arxiv.org/abs/chao-dyn/9511001v3

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Sep 23, 2013
09/13

by
Mark Srednicki

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We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.

Source: http://arxiv.org/abs/cond-mat/9406056v1

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Sep 17, 2013
09/13

by
Mark Srednicki

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We propose a resolution to the black-hole information-loss paradox: in one formulation of physical theory, information is preserved and macroscopic causality is violated; in another, causality is preserved and pure states evolve to mixed states. However, no experiments can be performed that would distinguish these two descriptions. We explain how this could work in practice; a key ingredient is the suggested quantum-chaotic nature of black holes.

Source: http://arxiv.org/abs/hep-th/0207090v1

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Sep 22, 2013
09/13

by
Mark Srednicki

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If a many-body quantum system approaches thermal equilibrium from a generic initial state, then the expectation value $\langle\psi(t)|A_i|\psi(t)\rangle$, where $|\psi(t)\rangle$ is the system's state vector and $A_i$ is an experimentally accessible observable, should approach a constant value which is independent of the initial state, and equal to a thermal average of $A_i$ at an appropriate temperature. We show that this is the case for all simple observables whenever the system is...

Source: http://arxiv.org/abs/cond-mat/9410046v2

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Jul 20, 2013
07/13

by
Mark Srednicki

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Phenomenological and formal restrictions on the evolution of pure into mixed states are discussed. In particular, it is argued that, if energy is conserved, loss of purity is incompatible with the weakest possible form of Lorentz covariance.

Source: http://arxiv.org/abs/hep-th/9206056v2

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Sep 17, 2013
09/13

by
Mark Srednicki

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We reconsider the question of the spectral statistics of the k-body random-interaction model, investigated recently by Benet, Rupp, and Weidenmueller, who concluded that the spectral statistics are Poissonian. The binary-correlation method that these authors used involves formal manipulations of divergent series. We argue that Borel summation does not suffice to define these divergent series without further (arbitrary) regularization, and that this constitutes a significant gap in the...

Source: http://arxiv.org/abs/cond-mat/0207201v1

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Sep 19, 2013
09/13

by
Mark Srednicki

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The ground state density matrix for a massless free field is traced over the degrees of freedom residing inside an imaginary sphere; the resulting entropy is shown to be proportional to the area (and not the volume) of the sphere. Possible connections with the physics of black holes are discussed.

Source: http://arxiv.org/abs/hep-th/9303048v2

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Sep 22, 2013
09/13

by
Mark Srednicki

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We consider Type IIB superstring theory with the addition of n 9-branes and n anti-9-branes (and no orientifolds). The result is a ten-dimensional chiral theory of open and closed oriented strings with gauge group U(n) \times U(n). There is, however, a tachyonic instability which can be understood as the consequence of brane-antibrane annihilation. We therefore expect to recover the usual IIB theory as the tachyon rolls to infinity.

Source: http://arxiv.org/abs/hep-th/9807138v2

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Sep 23, 2013
09/13

by
Mark Srednicki

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The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum hamiltonian. If so, conjectures by Katz and Sarnak put this hamiltonian in Altland and Zirnbauer's universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign...

Source: http://arxiv.org/abs/1105.2342v6

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Sep 18, 2013
09/13

by
Mark Srednicki

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I discuss the validity of the quantum Boltzmann equation for the calculation of WIMP relic densities.

Source: http://arxiv.org/abs/hep-ph/0005174v2

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Sep 20, 2013
09/13

by
Mark Srednicki; Frank Stiernelof

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We study the fluctuations that are predicted in the autocorrelation function of an energy eigenstate of a chaotic, two-dimensional billiard by the conjecture (due to Berry) that the eigenfunction is a gaussian random variable. We find an explicit formula for the root-mean-square amplitude of the expected fluctuations in the autocorrelation function. These fluctuations turn out to be $O(\hbar^{1/2})$ in the small $\hbar$ (high energy) limit. For comparison, any corrections due to scars from...

Source: http://arxiv.org/abs/chao-dyn/9603012v1

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7.0

Jun 29, 2018
06/18

by
Ben Michel; Mark Srednicki

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Calculations of the entanglement entropy of a spatial region in continuum quantum field theory require boundary conditions on the fields at the fictitious boundary of the region. These boundary conditions impact the treatment of the zero modes of the fields and their contribution to the entanglement entropy. We explore this issue in the simplest example, the c=1 compact-boson conformal field theory in 1+1 dimensions. We consider three different types of boundary conditions: spatial Neumann,...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1612.08682

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Sep 21, 2013
09/13

by
Marcos Rigol; Mark Srednicki

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An isolated quantum many-body system in an initial pure state will come to thermal equilibrium if it satisfies the eigenstate thermalization hypothesis (ETH). We consider alternatives to ETH that have been proposed. We first show that von Neumann's quantum ergodic theorem relies on an assumption that is essentially equivalent to ETH. We also investigate whether, following a sudden quench, special classes of pure states can lead to thermal behavior in systems that do not obey ETH, namely,...

Source: http://arxiv.org/abs/1108.0928v2

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Sep 20, 2013
09/13

by
Martin White; Mark Srednicki

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We discuss the applicability and derivation of window functions for cosmic microwave background experiments on large and intermediate angular scales. These window functions describe the response of the experiment to power in a particular mode of the fluctuation spectrum. We give general formulae, illustrated with specific examples, for the most common observing strategies.

Source: http://arxiv.org/abs/astro-ph/9402037v1

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Sep 17, 2013
09/13

by
Andrew Jordan; Mark Srednicki

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We study the quantum mechanics of a generalized version of the baker's map. We show that the Ruelle resonances (which govern the approach to ergodicity of classical distributions on phase space) also appear in the quantum correlation functions of observables at different times, and hence control the statistical variance of matrix elements of observables (in the basis of eigenstates of the quantum time evolution operator). We illustrate this with numerical results.

Source: http://arxiv.org/abs/nlin/0108024v2

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Sep 23, 2013
09/13

by
Anupam Singh; Mark Srednicki

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Starting from a Caldeira-Leggett model for the interaction of a system with an environment, Joichi, Matsumoto, and Yoshimura have reconsidered the derivation of the quantum Boltzmann equation. They find an extra term that accounts for the effects of virtual particles, and which drastically changes the results for relic densities of stable, weakly interacting massive particles (WIMPs), and for the decay products of unstable particles. We show, however, that this modified Boltzmann equation does...

Source: http://arxiv.org/abs/hep-ph/9908224v1

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Sep 22, 2013
09/13

by
Mark Srednicki; James Hartle

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As observers of the universe we are physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in spacetime. Predictions of our future observations therefore require an assumed probability distribution---the xerographic distribution---for our location among the possible ones. It is the combination of basic theory plus the xerographic distribution that can be...

Source: http://arxiv.org/abs/1004.3816v1

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Sep 18, 2013
09/13

by
Sanjay Hortikar; Mark Srednicki

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An energy eigenfunction in a classically chaotic system is known to have spatial correlations which (in the limit of small $\hbar$) are governed by a microcanonical distribution in the classical phase space. This result is valid, however, only over coordinate distances which are small compared to any relevant classical distance scales (such as the cyclotron radius for a charged particle in a magnetic field). We derive a modified formula for the correlation function in the regime of large...

Source: http://arxiv.org/abs/chao-dyn/9710025v1

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Sep 21, 2013
09/13

by
Sanjay Hortikar; Mark Srednicki

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The expected root-mean-square value of a matrix element $A_{\alpha\beta}$ in a classically chaotic system, where $A$ is a smooth, $\hbar$-independent function of the coordinates and momenta, and $\alpha$ and $\beta$ label different energy eigenstates, has been evaluated in the literature in two different ways: by treating the energy eigenfunctions as gaussian random variables and averaging $|A_{\alpha\beta}|^2$ over them; and by relating $|A_{\alpha\beta}|^2$ to the classical time-correlation...

Source: http://arxiv.org/abs/chao-dyn/9711020v1

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Sep 21, 2013
09/13

by
Anupam Singh; Mark Srednicki

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We present a general statistical analysis of Gamma Ray Bursts embedded in a host population. If no host generates more than one observed burst, then we show that there is a model independent lower bound on the number of hosts, $H$, of the form $H > c B^2$, where B is the number of observed bursts, and $c$ is a constant of order one which depends on the confidence level (CL) attached to the bound. An analysis by Tegmark et al. (1996) shows that the BATSE 3B catalog of 1122 bursts is...

Source: http://arxiv.org/abs/astro-ph/9705195v2

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Sep 22, 2013
09/13

by
Mark Srednicki; James Hartle

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As observers of the universe we are quantum physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in spacetime. The physical conditions at these locations that are not specified by the data may differ. Predictions of our future observations therefore require an assumed probability distribution (the xerographic distribution) for our location among the possible...

Source: http://arxiv.org/abs/0906.0042v3

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Sep 23, 2013
09/13

by
Sanjay Hortikar; Mark Srednicki

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We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit corrections; each orbit is weighted by the usual Gutzwiller factor times $A_p B_p ...$, where $A_p$ is the average of the classical observable $A$ along the periodic orbit $p$. This structure for the orbit corrections was previously proposed by Main and Wunner...

Source: http://arxiv.org/abs/chao-dyn/9908009v2

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47

Sep 18, 2013
09/13

by
James B. Hartle; Mark Srednicki

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Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by some physical process, despite the absence of any evidence for such a process, or any observational evidence favoring our typicality. It is possible to favor theories in which we are typical by appropriately choosing their prior probabilities, but such...

Source: http://arxiv.org/abs/0704.2630v3

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Sep 17, 2013
09/13

by
Steven B. Giddings; Mark Srednicki

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Aspects of super-planckian gravitational scattering and black hole formation are investigated, largely via a partial-wave representation. At large and decreasing impact parameters, amplitudes are expected to be governed by single graviton exchange, and then by eikonalized graviton exchange, for which partial-wave amplitudes are derived. In the near-Schwarzschild regime, perturbation theory fails. However, general features of gravitational scattering associated with black hole formation suggest...

Source: http://arxiv.org/abs/0711.5012v2

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5.0

Jun 27, 2018
06/18

by
Keith R. Fratus; Mark Srednicki

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A strongly non-integrable system is expected to satisfy the eigenstate thermalization hypothesis, which states that the expectation value of an observable in an energy eigenstate is the same as the thermal value. This must be revised if the observable is an order parameter for a spontaneously broken symmetry, which has multiple thermal values. We propose that in this case the system is unstable towards forming nearby eigenstates which yield each of the allowed thermal values. We provide strong...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1505.04206

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Sep 21, 2013
09/13

by
Douglas Scott; Mark Srednicki; Martin White

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We discuss the effects of finite sky coverage and the uncertainty in extracting information about the power spectrum from experiments on small angular scales. In general the cosmic variance is enhanced by a factor of $4\pi/A$, where $A$ is the solid angle sampled by the experiment. As a rough guide, an experiment with sensitivity peaking at the $\ell$th multipole has to cover $\simgt\ell$ independent patches to have a lower ``sample variance'' than for a whole-sky measurement of the quadrupole....

Source: http://arxiv.org/abs/astro-ph/9305030v2

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Sep 20, 2013
09/13

by
Toby Falk; Raghavan Rangarajan; Mark Srednicki

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In the standard inflationary scenario with inflaton potential $V(\Phi)=M^4-{1\over4}\lambda\Phi^4$, the resulting density perturbations $\delta\rho/\rho$ are proportional to $\lambda^{1/2}$. Upper bounds on $\delta\rho/\rho$ require $\lambda < 10^{-13}$. Ratra has shown that an alternative treatment of reheating results in $\delta\rho/\rho \propto \lambda^{-1}$, so that an upper bound on $\delta\rho/\rho$ does not put an obvious upper bound on $\lambda$. We verify that $\delta\rho/\rho...

Source: http://arxiv.org/abs/astro-ph/9208002v1

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Sep 24, 2013
09/13

by
Toby Falk; Raghavan Rangarajan; Mark Srednicki

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Inflationary models predict a definite, model independent, angular dependence for the three-point correlation function of $\Delta T/T$ at large angles (greater than $\sim 1^\circ$) which we calculate. The overall amplitude is model dependent and generically unobservably small, but may be large in some specific models. We compare our results with other models of nongaussian fluctuations.

Source: http://arxiv.org/abs/astro-ph/9208001v1

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Sep 19, 2013
09/13

by
Edward W. Kolb; Anupam Singh; Mark Srednicki

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We study the time evolution of the quantum fluctuations of the axion field for both the QCD axion as well as axions arising in the context of supergravity and string theories. We explicitly keep track not only of the coherently oscillating zero momentum mode of the axion but also of the higher non-zero momentum modes using the full axion potential. The full axion potential makes possible two kinds of instabilities: spinodal instabilities and parametric resonance instabilities. The presence of...

Source: http://arxiv.org/abs/hep-ph/9709285v2

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Sep 18, 2013
09/13

by
Donald Marolf; Ian A. Morrison; Mark Srednicki

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We construct a perturbative S-matrix for interacting massive scalar fields in global de Sitter space. Our S-matrix is formulated in terms of asymptotic particle states in the far past and future, taking appropriate care for light fields whose wavefunctions decay only very slowly near the de Sitter conformal boundaries. An alternative formulation expresses this S-matrix in terms of residues of poles in analytically-continued Euclidean correlators (computed in perturbation theory), making it...

Source: http://arxiv.org/abs/1209.6039v3

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Sep 22, 2013
09/13

by
Toby Falk; Keith A. Olive; Mark Srednicki

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We calculate the relic density of very heavy, stable scalar neutrinos in the minimal supersymmetric standard model. We include all two-body final states, as well as the effects of co-annihilation with scalar electrons. We find that the sneutrino relic density is in the cosmologically interesting region $0.1\ltwid\Omega_{\sn}h^2\ltwid 1.0$ for $550\gev\ltwid\msn\ltwid 2300\gev$. For nominal values of the parameters of our galactic halo, recent results from the Heidelberg--Moscow direct detection...

Source: http://arxiv.org/abs/hep-ph/9409270v1

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Sep 20, 2013
09/13

by
Alexandre Dolgov; Katherine Freese; Raghavan Rangarajan; Mark Srednicki

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We calculate the baryon asymmetry created by the decay of a pseudo Nambu-Goldstone boson whose interactions violate baryon number conservation. Our results are in disagreement with previous results in the original spontaneous baryogenesis models for the asymmetry produced by the decay of an oscillating scalar field with B number violating derivative couplings; we find that the net baryon number density is proportional to $\th_i^3$, where $\th_i$ is the amplitude of the PNGB-field in natural...

Source: http://arxiv.org/abs/hep-ph/9610405v1

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Jul 20, 2013
07/13

by
Ehsan Khatami; Guido Pupillo; Mark Srednicki; Marcos Rigol

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We examine the validity of fluctuation-dissipation relations in isolated quantum systems taken out of equilibrium by a sudden quench. We focus on the dynamics of trapped hard-core bosons in one-dimensional lattices with dipolar interactions whose strength is changed during the quench. We find that fluctuation-dissipation relations hold if the system is nonintegrable after the quench. They also hold if the system is integrable after the quench if the initial state is an equilibrium state of a...

Source: http://arxiv.org/abs/1304.7279v1

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Sep 20, 2013
09/13

by
Toby Falk; Richard Madden; Keith A. Olive; Mark Srednicki

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We calculate the one-loop contribution to the bino annihilation rate due to the process $\widetilde B \widetilde B \to Z^*$, which vanishes at tree level.

Source: http://arxiv.org/abs/hep-ph/9402233v1

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Sep 19, 2013
09/13

by
Mark Srednicki; Martin White; Douglas Scott; Emory T. Bunn

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We analyze the Gamma Ursae Minoris (GUM) and Mu Pegasii (MuP) scans of the Millimeter-wave Anisotropy eXperiment in the context of cold dark matter (CDM) models of structure formation, paying particular attention to the two-dimensional nature of the GUM scan. If all of the structure in the (foreground subtracted) data is attributed to cosmic microwave background anisotropy, then there is a detection in each scan. For a standard CDM model, the amplitudes of the signals are individually...

Source: http://arxiv.org/abs/astro-ph/9309006v1

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Sep 18, 2013
09/13

by
Toby Falk; Keith A. Olive; Leszek Roszkowski; Mark Srednicki

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We consider the Minimal Supersymmetric Standard Model (MSSM) without imposing relations on the superpartner masses that arise in grand unified theories. Given an arbitrary pattern of superpartner masses (consistent with experimental constraints), it may happen that the scalar potential is actually unstable, even though all scalar masses-squared are positive at the weak scale $M_W$. This is most likely to happen if the running mass-squared in a ``flat'' direction in field space becomes negative...

Source: http://arxiv.org/abs/hep-ph/9510308v1

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Sep 20, 2013
09/13

by
Toby Falk; Richard Madden; Keith A. Olive; Mark Srednicki

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We consider corrections to bino annihilation due to sfermion mixing.

Source: http://arxiv.org/abs/hep-ph/9308324v1

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Jun 28, 2018
06/18

by
Rubem Mondaini; Keith R. Fratus; Mark Srednicki; Marcos Rigol

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We study the onset of eigenstate thermalization in the two-dimensional transverse field Ising model (2D-TFIM) in the square lattice. We consider two non-equivalent Hamiltonians: the ferromagnetic 2D-TFIM and the antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. We use full exact diagonalization to examine the behavior of quantum chaos indicators and of the diagonal matrix elements of operators of interest in the eigenstates of the Hamiltonian. A finite size scaling...

Topics: Quantum Physics, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1512.04947