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Mark Srednicki

Publications and source records attributed to Mark Srednicki.

At least 37 records · Page 2Linked to original sources
arXiv2011

The Berry-Keating Hamiltonian and the Local Riemann Hypothesis

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 conjecture. The p-adic case is also discussed.

math-ph↗
arXiv2010

Science in a Very Large Universe

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 ones. It is the combination of basic theory plus the xerographic distribution that can be predictive and testable by further observations.

hep-th↗
arXiv2010

The Xerographic Distribution: Scientific Reasoning in a Large Universe

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 predictive and testable by further observations. This is illustrated by examining a toy model of a classical deterministic universe with a fixed flat metric.

hep-th↗
arXiv2008

Against Tachyophobia

We examine the possible extension of the parameter space of the minimal supersymmetric extension of the Standard Model (MSSM), as expressed via the renormalization-group equations in terms of universal soft supersymmetry-breaking terms at the unification scale, to include tachyonic input scalar masses. Many models with negative masses-squared for scalars at the unification scale may be viable because the small sizes of the masses-squared allow them to change signs during the renormalization-group evolution to the electroweak scale. However, in many cases, there is, in addition to the electroweak vacuum, a much deeper high-scale vacuum located along some F- and D-flat direction in the effective potential for the MSSM. We perform a numerical search for such vacua in both the CMSSM and the NUHM. We discuss the circumstances under which the existence of such a deep charge- and color-breaking vacuum is consistent with standard cosmology. A crucial role is played by the inflation--induced scalar masses, whereas thermal effects are often irrelevant.

hep-ph↗
arXiv2008

High-energy gravitational scattering and black hole resonances

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 a particular form for amplitudes, which we express as a black hole ansatz. We explore features of this ansatz, including its locality properties. These amplitudes satisfy neither the Froissart bound, nor apparently the more fundamental property of polynomial boundedness, through which locality is often encoded in an S-matrix framework. Nevertheless, these amplitudes do satisfy a macroscopic form of causality, expressed as a polynomial bound for the forward-scattering amplitude.

hep-th↗
arXiv2007

Are We Typical?

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 assumptions should be made explicit to avoid confusion.

hep-th↗
arXiv2005

Subjective and Objective Probabilities in Quantum Mechanics

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.

quant-ph↗
arXiv2002

Axions: Past, Present, and Future

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.

hep-th↗
arXiv2002

On the Observability of Quantum Information Radiated from a Black Hole

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.

hep-th↗
arXiv2002

Spectral statistics of the k-body random-interaction model

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 demonstration of Poissonian statistics. Our conclusion is that the spectral statistics of the k-body random-interaction model remains an open question.

cond-mat.stat-mech↗
arXiv2001

Sub-Planck Structure, Decoherence, and Many-Body Environments

In a recent paper [Nature 412, 712 (2001)], Zurek has argued that (1) time evolution typically causes chaotic quantum systems to generate structure that varies on the scale of phase-space volume elements of size $(\hbar^2/A)^d$, where A is a classical action characteristic of the state and d is the number of degrees of freedom, and that (2) this structure implies that a small change in a phase-space coordinate X by an amount $δX \sim \hbar X/A$ generically results in an orthogonal state. While we agree with (1), we argue that (2) is not correct if the number of degrees of freedom is small. Our arguments are based on the Berry-Voros ansatz for the structure of energy eigenstates in chaotic systems. We find, however, that (2) becomes valid if the number of degrees of freedom is large. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence.

quant-ph↗
arXiv2001

The Approach to Ergodicity in the Quantum Baker's Map

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.

nlin.CD↗
arXiv2000

Thermal Abundances of Heavy Particles

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 carry a conserved U(1) charge, and the light particles do not. The fluctuations of the net charge in a given volume then provide a measure of the total number of heavy particles in that same volume. We show that these charge fluctuations are Boltzmann suppressed (to all orders in perturbation theory). Therefore, we argue, the number density of heavy particles is also Boltzmann suppressed.

hep-ph↗
arXiv1999

A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems

We derive a trace formula for $\sum_n A_{nn}B_{nn}...δ(E-E_n)$, 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 (chao-dyn/9904040) on the basis of numerical evidence.

chao-dyn↗
arXiv1999

Quantum Kinetic Equations and Dark Matter Abundances Reconsidered

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 not properly account for the interaction energy between the massive particles (which are decaying or annihilating) and the thermal bath of light particles. We argue that the conventional Boltzmann equation gives the correct result.

hep-ph↗