Nonzero Energy Density Research Articles

Eigenstate Localization in a Many-Body Quantum System.

We prove the existence of extensive many-body Hamiltonians with few-body interactions and a many-body mobility edge: all eigenstates below a nonzero energy density are localized in an exponentially small fraction of "energetically allowed configurations" within Hilbert space. Our construction is based on quantum perturbations to a classical low-density parity check code. In principle, it is possible to detect this eigenstate localization by measuring few-body correlation functions in efficiently preparable mixed states.

The Q‐Space Deformed Wave Equation

Let q ∈ (0,1). We know that, when q tends to 1, we recover “classical” quantum mechanics. However, when q is not equal to one, we have a theory of quantum mechanics in a spacetime, i.e., a theory where the vacuum has a nonzero energy density. As a q‐analogue on the space variable of the wave equation, we introduce the q‐space wave equation. Solutions of these equations are given for q ∈ (0,1) and for q⟶0. Since some states have more spin degrees of freedom than the physical particle has, the q‐space wave equations remove the additional degrees of freedom.

Tracking the many-body localized to ergodic transition via extremal statistics of entanglement eigenvalues

Some interacting disordered many-body systems are unable to thermalize when the quenched disorder becomes larger than a threshold value. Although several properties of nonzero energy density eigenstates (in the middle of the many-body spectrum) exhibit a qualitative change across this many-body localization (MBL) transition, many of the commonly-used diagnostics only do so over a broad transition regime. Here, we provide evidence that the transition can be located precisely even at modest system sizes by sharply-defined changes in the distribution of extremal eigenvalues of the reduced density matrix of subsystems. In particular, our results suggest that $p* = \lim_{\lambda_2 \rightarrow \ln(2)^{+}}P_2(\lambda_2)$, where $P_2(\lambda_2)$ is the probability distribution of the second lowest entanglement eigenvalue $\lambda_2$, behaves as an ''order-parameter'' for the MBL phase: $p*> 0$ in the MBL phase, while $p* = 0$ in the ergodic phase with thermalization. Thus, in the MBL phase, there is a nonzero probability that a subsystem is entangled with the rest of the system only via the entanglement of one subsystem qubit with degrees of freedom outside the region. In contrast, this probability vanishes in the thermal phase.

Cosmological decoherence from thermal gravitons

We study the effects of gravitationally-driven decoherence on tunneling processes associated with false vacuum decays, such as the Coleman-De Luccia instanton. We compute the thermal graviton-induced decoherence rate for a wave function describing a perfect fluid of nonzero energy density in a finite region. When the effective cosmological constant is positive, the thermal graviton background sourced by a de Sitter horizon provides an unavoidable decoherence effect, which may have important consequences for tunneling processes in cosmological history. We discuss generalizations and consequences of this effect and comment on its observability and applications to black hole physics.

Accelerating imperfect fluid

An inhomogeneous fluid in accelerated motion is investigated. When the velocity field v(x) is not constant, the geometry viewed by a static observer is curved, as if the observer were immersed in a gravitational field. A velocity-dependent semiclassical gravitational potential is introduced, which obeys an Yukawa-type equation, written in Cartesian coordinates. The timelike and null geodesic equations are investigated. One finds that the fluid has zero energy density corresponding to the perfect fluid part but nonzero anisotropic energy density. The pressures will no longer depend on ħ for time intervals t>>1/m, where m is the field mass.

Structure of chaotic eigenstates and their entanglement entropy.

We consider a chaotic many-body system (i.e., one that satisfies the eigenstate thermalization hypothesis) that is split into two subsystems, with an interaction along their mutual boundary, and study the entanglement properties of an energy eigenstate with nonzero energy density. When the two subsystems have nearly equal volumes, we find a universal correction to the entanglement entropy that is proportional to the square root of the system's heat capacity (or a sum of capacities, if there are conserved quantities in addition to energy). This phenomenon was first noted by Vidmar and Rigol in a specific system; our analysis shows that it is generic, and expresses it in terms of thermodynamic properties of the system. Our conclusions are based on a refined version of a model of a chaotic eigenstate originally due to Deutsch, and analyzed more recently by Lu and Grover.

Spin and orbital angular momenta of acoustic beams

We analyze spin and orbital angular momenta in monochromatic acoustic wave fields in a homogeneous medium. Despite being purely longitudinal (curl-free), inhomogeneous acoustic waves generically possess nonzero spin angular momentum density caused by the local rotation of the vector velocity field. We show that the integral spin of a localized acoustic wave vanishes in agreement with the spin-0 nature of longitudinal phonons. We also show that the helicity or chirality density vanishes identically in acoustic fields. As an example, we consider nonparaxial acoustic Bessel beams carrying well-defined integer orbital angular momentum, as well as nonzero local spin density, with both transverse and longitudinal components. We describe the nontrivial polarization structure in acoustic Bessel beams and indicate a number of observable phenomena, such as nonzero energy density and purely-circular transverse polarization in the center of the first-order vortex beams.

Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis

We obtain multiple exact results on the entanglement of the exact excited states of non-integrable models we introduced in arXiv:1708.05021. We first discuss a general formalism to analytically compute the entanglement spectra of exact excited states using Matrix Product States and Matrix Product Operators and illustrate the method by reproducing a general result on single-mode excitations. We then apply this technique to analytically obtain the entanglement spectra of the infinite tower of states of the spin-$S$ AKLT models in the zero and finite energy density limits. We show that in the zero density limit, the entanglement spectra of the tower of states are multiple shifted copies of the ground state entanglement spectrum in the thermodynamic limit. We show that such a resemblance is destroyed at any non-zero energy density. Furthermore, the entanglement entropy $\mathcal{S}$ of the states of the tower that are in the bulk of the spectrum is sub-thermal $\mathcal{S} \propto \log L$, as opposed to a volume-law $\mathcal{S} \propto L$, thus indicating a violation of the strong Eigenstate Thermalization Hypothesis (ETH). These states are examples of what are now called many-body scars. Finally, we analytically study the finite-size effects and symmetry-protected degeneracies in the entanglement spectra of the excited states, extending the existing theory.

The effect of a two-fluid atmosphere on relativistic stars

We model the physical behaviour at the surface of a relativistic radiating star in the strong gravity limit. The spacetime in the interior is taken to be spherically symmetrical and shear-free. The heat conduction in the interior of the star is governed by the geodesic motion of fluid particles and a non-vanishing radially directed heat flux. The local atmosphere in the exterior region is a two-component system consisting of standard pressureless (null) radiation and an additional null fluid with non-zero pressure and constant energy density. We analyse the generalised junction condition for the matter and gravitational variables on the stellar surface and generate an exact solution. We investigate the effect of the exterior energy density on the temporal evolution of the radiating fluid pressure, luminosity, gravitational redshift and mass flow at the boundary of the star. The influence of the density on the rate of gravitational collapse is also probed and the strong, dominant and weak energy conditions are also tested. We show that the presence of the additional null fluid has a significant effect on the dynamical evolution of the star.

Zero Point Energy Effects on Quantum Electrodynamics

The vacuum is not a state of empty space, but is populated by electromagnetic fluctuations at a lowest nonzero level, the Zero Point Energy (ZPE). As distinguished from conventional theories, such as that of the Standard Model, the present revised quantum electrodynamic theory (RQED) includes the ZPE in its field equations. This leads to new results far beyond those obtained from conventional theories such as those by Dirac and Higgs. Thus, the present theory results in massive elementary particles from the beginning, being independent of the theory by Higgs. This paper describes the background and results of RQED, summarizing the weak points of conventional theories, the unification of included fundamental concepts, the present basic field equations, new obtained results, and special points of experimental support. In other words, the new points stressed in this paper are in particular the relation between a nonzero electric field divergence in the vacuum and the ZPE, and a number of new experimentally supported results due to a nonzero ZPE energy density in the same state.

Marginal Anderson localization and many-body delocalization

We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent \nu. This class includes disordered systems with intrinsic- or symmetry-protected- topological bands, such as disordered integer quantum Hall insulators. In the absence of interactions, such marginally localized systems exhibit anomalous properties intermediate between localized and extended including: vanishing DC conductivity but sub-diffusive dynamics, and fractal entanglement (an entanglement entropy with a scaling intermediate between area and volume law). We investigate the stability of marginal localization in the presence of interactions, and argue that arbitrarily weak short range interactions trigger delocalization for partially filled bands at non-zero energy density if \nu \ge 1/d. We use the Harris/Chayes bound \nu \ge 2/d, to conclude that marginal localization is generically unstable in the presence of interactions. Our results suggest the impossibility of stabilizing quantized Hall conductance at non-zero energy density.

Analyzing Many-Body Localization with a Quantum Computer

Many-body localization, the persistence against electron-electron interactions of the localization of states with non-zero excitation energy density, poses a challenge to current methods of theoretical and numerical analysis. Numerical simulations have so far been limited to a small number of sites, making it difficult to obtain reliable statements about the thermodynamic limit. In this paper, we explore the ways in which a relatively small quantum computer could be leveraged to study many-body localization. We show that, in addition to studying time-evolution, a quantum computer can, in polynomial time, obtain eigenstates at arbitrary energies to sufficient accuracy that localization can be observed. The limitations of quantum measurement, which preclude the possibility of directly obtaining the entanglement entropy, make it difficult to apply some of the definitions of many-body localization used in the recent literature. We discuss alternative tests of localization that can be implemented on a quantum computer.

Area laws in a many-body localized state and its implications for topological order

The question whether Anderson insulators can persist to finite-strength interactions—a scenario dubbed many-body localization—has recently received a great deal of interest. The origin of such a many-body localized phase has been described as localization in Fock space, a picture we examine numerically. We then formulate a precise sense in which a single energy eigenstate of a Hamiltonian can be adiabatically connected to a state of a non-interacting Anderson insulator. We call such a state a many-body localized state and define a many-body localized phase as one in which almost all states are many-body localized states. We explore the possible consequences of this; the most striking is an area law for the entanglement entropy of almost all excited states in a many-body localized phase. We present the results of numerical calculations for a one-dimensional system of spinless fermions. Our results are consistent with an area law and, by implication, many-body localization for almost all states and almost all regions for weak enough interactions and strong disorder. However, there are rare regions and rare states with much larger entanglement entropies. Furthermore, we study the implications that many-body localization may have for topological phases and self-correcting quantum memories. We find that there are scenarios in which many-body localization can help to stabilize topological order at non-zero energy density, and we propose potentially useful criteria to confirm these scenarios.

DARK ENERGY DENSITY IN MODELS WITH SPLIT SUPERSYMMETRY AND DEGENERATE VACUA

In N = 1 supergravity supersymmetric and nonsupersymmetric Minkowski vacua originating in the hidden sector can be degenerate. In the supersymmetric phase in flat Minkowski space, nonperturbative supersymmetry breakdown may take place in the observable sector, inducing a nonzero and positive vacuum energy density. Assuming that such a supersymmetric phase and the phase in which we live are degenerate, we estimate the value of the cosmological constant. We argue that the observed value of the dark energy density can be reproduced in the split SUSY scenario of SUSY breaking if the SUSY breaking scale is of order of 1010 GeV.

Negative vacuum energy densities and the causal diamond measure

Arguably a major success of the landscape picture is the prediction of a small, non-zero vacuum energy density. The details of this prediction depends in part on how the diverging spacetime volume of the multiverse is regulated, a question that remains unresolved. One proposal, the causal diamond measure, has demonstrated many phenomenological successes, including predicting a distribution of positive vacuum energy densities in good agreement with observation. In the string landscape, however, the vacuum energy density is expected to take positive and negative values. We find the causal diamond measure gives a poor fit to observation in such a landscape -- in particular, 99.6% of observers in galaxies seemingly just like ours measure a vacuum energy density smaller than we do, most of them measuring it to be negative.

Modeling heavy ion collisions in AdS/CFT

We construct a model of high energy heavy ion collisions as two ultrarelativistic shock waves colliding in AdS5. We point out that shock waves corresponding to physical energy-momentum tensors of the nuclei completely stop almost immediately after the collision in AdS5, which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Since in real-life heavy ion collisions the large Bjorken x part of nuclear wave functions continues to move along the light cone trajectories of the incoming nuclei leaving the small-x partons behind, we conclude that a pure large coupling approach is not likely to adequately model nuclear collisions. We show that to account for small-coupling effects one can model the colliding nuclei by two (unphysical) ultrarelativistic shock waves with zero net energy each (but with non-zero energy density). We use this model to study the energy density of the strongly-coupled matter created immediately after the collision. We argue that expansion of the energy density in the powers of proper time τ squared corresponds on the gravity side to a perturbative expansion of the metric in graviton exchanges. Using such expansion we reproduce our earlier result [1] that the energy density of produced matter at mid-rapidity starts out as a constant (of time) in heavy ion collisions at large coupling.

Evolution of Bouncing Cosmological Models Due to the Self-Gravitational Corrections

A four-dimensional timelike brane with non-zero energy density is considered as the boundary of a five dimensional Schwarzschild anti de Sitter bulk background. The self-gravitational corrections to the first Friedmann equation act as a source of stiff matter contrary to standard FRW cosmology where the charge of the black hole plays this role. In a previous related paper (Setare in Eur. Phys. J. C 47:851, [2006]), bouncing cosmology was studied, from a holographic perspective, for the very special case of a brane that is void of any intrinsic matter sources. In this paper we extend the results of (Setare in Eur. Phys. J. C 47:851, [2006]). We consider the physically relevant case in which a perfect fluid with equation of state of radiation is present on the brane. Then, we describe solutions of the braneworld theory under investigation and also determine their stability. Specifically, if we do not consider the self-gravitational corrections, the AdS black hole with zero ADM mass, and open horizon is an attractor, while, if we consider, the AdS black hole with zero ADM mass and flat horizon, and D3-brane with non-zero energy density is a repeller.

Test of [formula omitted] local gauge invariance in Proca electrodynamics

An experiment for testing U ( 1 ) local gauge invariance in Proca electrodynamics has been performed by a rotating toroidal coil torsion pendulum. The expected signal, presented as the nonzero energy density of the magnetic filed vector potentials, is sought and a null result is obtained, showing the U ( 1 ) symmetry being tightly held presently.

The self-gravitational corrections as the source for stiff matter on the brane in [formula omitted] bulk

A D3-brane with non-zero energy density is considered as the boundary of a five-dimensional Schwarzschild–anti-de Sitter bulk background. Taking into account the semi-classical corrections to the black hole entropy that arise as a result of the self-gravitational effect, and employing the AdS/CFT correspondence, we obtain the self-gravitational correction to the first Friedmann-like equation. The additional term in the Hubble equation due to the self-gravitational effect goes as a−6. Thus, the self-gravitational corrections act as a source of stiff matter contrary to standard FRW cosmology where the charge of the black hole plays this role.

DIRAC MONOPOLES AND HAWKING RADIATION IN KOTTLER SPACETIME

The natural extension of Schwarzschild metric to the case of nonzero cosmological constant Λ known as the Kottler metric is considered and it is discussed under what circumstances the given metric could describe the Schwarzschild black hole immersed in a medium with nonzero energy density. Under the latter situation such an object might carry topologically inequivalent configurations of various fields. The given possibility is analyzed for complex scalar field and it is shown that the mentioned configurations might be tied with natural presence of Dirac monopoles on black hole under consideration. In turn, this could markedly modify the Hawking radiation process.