Searcharxiv⌕ Search

arXiv subjects

Mark Srednicki

Publications and source records attributed to Mark Srednicki.

At least 55 records · Page 3Linked to original sources
arXiv1998

The approach to thermal equilibrium in quantized chaotic systems

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 nonequilibrium expectation value at some particular moment, then it is overwhelmingly likely to move towards equilibrium, both forwards and backwards in time. For deviations from equilibrium that are not much larger than a typical quantum or thermal fluctuation, we find that the time dependence of the move towards equilibrium is given by the Kubo correlation function, in agreement with Onsager's postulate. These results are independent of the details of the system's quantum state.

cond-mat.stat-mech↗
arXiv1998

IIB or not IIB

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.

hep-th↗
arXiv1998

Quantum Fluctuations of Axions

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 either of these instabilities can lead to a quasi-exponential increase in the occupation of non-zero momentum modes and the build-up of the quantum fluctuations of the axions. If either of these becomes a significant effect then axions would no longer be a suitable cold dark matter candidate. Our results confirm the conventional wisdom that these effects are not significant in the setting of an expanding FRW universe and hence axions are indeed cold dark matter candidates.

hep-ph↗
arXiv1997

Spatial Correlations in Chaotic Eigenfunctions

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.

chao-dyn↗
arXiv1997

Random Matrix Elements and Eigenfunctions in Chaotic Systems

The expected root-mean-square value of a matrix element $A_{αβ}$ in a classically chaotic system, where $A$ is a smooth, $\hbar$-independent function of the coordinates and momenta, and $α$ and $β$ 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 $|A_{αβ}|^2$ over them; and by relating $|A_{αβ}|^2$ to the classical time-correlation function of $A$. We show that these two methods give the same answer only if Berry's formula for the spatial correlations in the energy eigenfunctions (which is based on a microcanonical density in phase space) is modified at large separations in a manner which we previously proposed.

chao-dyn↗
arXiv1997

Correlations in Chaotic Eigenfunctions at Large Separation

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 separation. This then permits a complete description, over all length scales, of the statistical properties of chaotic eigenfunctions in the $\hbar\to 0$ limit. Applications to quantum dots are briefly discussed.

chao-dyn↗
arXiv1997

A model independent lower limit on the number of Gamma Ray Burst hosts from repeater statistics

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 consistent with no repeaters being present, and assuming that this is indeed the case, our result implies a host population with at least H=1.2x10^6 members. Without the explicit assumption of no repeaters, a Bayesian analysis based on the results of Tegmark et al. (1996) can be performed which gives the weaker bound of $H>1.7\times 10^5$ at the 90% CL. In the light of the non-detection of identifiable hosts in the small error-boxes associated with transient counterparts to GRBs, this result gives a model independent lower bound to the number of any rare or exotic hosts. If in fact GRBs are found to be associated with a particular sub-class of galaxies, then an analysis along the lines presented here can be used to place a lower bound on the fraction of galaxies in this sub-class. Another possibility is to treat galaxy clusters (rather than individual galaxies) as the host population, provided that the angular size of each cluster considered is less than the resolution of the detector. Finally, if repeaters are ever detected in a statistically significant manner, this analysis can be readily adapted to find upper and lower limits on $H$.

astro-ph↗
arXiv1996

Constraints from Inflation and Reheating on Superpartner Masses

Flat directions in the Minimal Supersymmetric Standard Model (MSSM) can become unstable due to radiative corrections, and the global minimum of the (zero temperature) potential can lie at large values of the squark and/or slepton fields. Here we show that, in inflationary models of early cosmology, the universe is very likely to be in the domain of attraction of this global minimum at the end of inflation. While the minimum at the origin of field space is global at sufficiently high temperatures, depending on details of the model, the universe may be trapped in the non-zero minimum until it becomes the global minimum at low temperatures. Parameter values leading to this scenario are therefore ruled out.

hep-ph↗
arXiv1996

Baryogenesis During Reheating in Natural Inflation and Comments on Spontaneous Baryogenesis

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 $þ_i^3$, where $þ_i$ is the amplitude of the PNGB-field in natural inflation at the onset of reheating. We also discuss our disagreement with the interpretation of $\dotθ$ as an effective chemical potential for baryon number in spontaneous baryogenesis models. While our calculation of the asymmetry is carried out in the context of natural inflation our approach is generally valid for baryogenesis models using decaying classical fields. In the Appendices, we include a complete derivation of the number density of particles produced by the decay of a classical scalar field; this number density is proportional to the integral over momenta of the one pair production amplitude.

hep-ph↗
arXiv1996

The Onset of Chaos in the Quantum Hard-Sphere Gas

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 $λ\ll \ell$, where $λ$ is the wavelength of a typical particle and $\ell$ is the mean free path between collisions. For fermions with Fermi wavelength $λ_F \ll \ell$, this implies that all energy eigenstates, including the ground state, are chaotic. Physical implications are discussed.

cond-mat↗
arXiv1996

Gaussian Fluctuations in Chaotic Eigenstates

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 isolated periodic orbits would also be $O(\hbar^{1/2})$. The fluctuations take on a particularly simple form if the autocorrelation function is averaged over the direction of the separation vector. We compare our various predictions with recent numerical computations of Li and Robnik for the Robnik billiard, and find good agreement. We indicate how our results generalize to higher dimensions.

chao-dyn↗
arXiv1995

Thermal Fluctuations in Quantized Chaotic Systems

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 $ΔE$ 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) the time variations of $ - \overline A$ are too small to represent thermal fluctuations; (3) however, the time variations of $ - ^2$ can be consistently interpreted as thermal fluctuations, even though these same time variations would be called quantum fluctuations when $N$ is small.

chao-dyn↗
arXiv1995

New Constraints on Superpartner Masses

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 at some scale $Q_0$ which is well below the GUT scale. In this case, either this pattern of masses is ruled out, or there must be new physics (beyond the MSSM) at or below the scale $Q_0$.

hep-ph↗
arXiv1995

Does Quantum Chaos Explain Quantum Statistical Mechanics?

If a many-body quantum system approaches thermal equilibrium from a generic initial state, then the expectation value $\langleψ(t)|A_i|ψ(t)\rangle$, where $|ψ(t)\rangle$ 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 classically chaotic.

cond-mat↗
arXiv1995

Phases in the MSSM, Electric Dipole Moments and Cosmological Dark Matter

We consider the effect of CP violating phases in the MSSM on the relic density of the lightest supersymmetric particle (LSP). In particular, we find that the upper limits on the LSP mass are relaxed when phases in the MSSM are allowed to take non-zero values when the LSP is predominantly a gaugino (bino). Previous limits of $\mb \la 250$ GeV for $Ωh^2 < 0.25$ can be relaxed to $\mb \la 650$ GeV. We also consider the additional constraints imposed by the neutron and electron electric dipole moments induced by these phases. Though there is some restriction on the phases, the bino mass may still be as large as $\sim$ 350 GeV and certain phases can be arbitrarily large.

hep-ph↗
arXiv1994

Heavy Sneutrinos as Dark Matter

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 $0.1\ltwidΩ_{\sn}h^2\ltwid 1.0$ 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 experiment set an upper limit on $Ω_{\sn}$ which is lower by a factor ranging from two to ten, depending on $\msn$.

hep-ph↗
arXiv1994

Quantum Chaos and Statistical Mechanics

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.

cond-mat↗