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At least 235 records · Page 13Linked to original sources
arXiv2011

Hard and soft walls

In a continuing effort to understand divergences which occur when quantum fields are confined by bounding surfaces, we investigate local energy densities (and the local energy-momentum tensor) in the vicinity of a wall. In this paper, attention is largely confined to a scalar field. If the wall is an infinite Dirichlet plane, well known volume and surface divergences are found, which are regulated by a temporal point-splitting parameter. If the wall is represented by a linear potential in one coordinate $z$, the divergences are softened. The case of a general wall, described by a potential of the form $z^α$ for $z>0$ is considered. If $α>2$, there are no surface divergences, which in any case vanish if the conformal stress tensor is employed. Divergences within the wall are also considered.

hep-th↗
arXiv2011

Thermal diffractive corrections to Casimir energies

We study the interplay of thermal and diffractive effects in Casimir energies. We consider plates with edges, oriented either parallel or perpendicular to each other, as well as a single plate with a slit. We compute the Casimir energy at finite temperature using a formalism in which the diffractive effects are encoded in a lower dimensional non-local field theory that lives in the gap between the plates. The formalism allows for a clean separation between direct or geometric effects and diffractive effects, and makes an analytic derivation of the temperature dependence of the free energy possible. At low temperatures, with Dirichlet boundary conditions on the plates, we find that diffractive effects make a correction to the free energy which scales as T^6 for perpendicular plates, as T^4 for slits, and as T^4 log T for parallel plates.

hep-th↗
arXiv2012

Born in an Infinite Universe: a Cosmological Interpretation of Quantum Mechanics

We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square of the wave function amplitudes. Our formal argument hinges on properties of what we term the quantum confusion operator, which projects onto the Hilbert subspace where the Born rule fails, and we comment on its relation to the oft-discussed quantum frequency operator. This analysis unifies the classical and quantum levels of parallel universes that have been discussed in the literature, and has implications for several issues in quantum measurement theory. It also shows how, even for a single measurement, probabilities may be interpreted as relative frequencies in unitary (Everettian) quantum mechanics. We also argue that after discarding a zero-norm part of the wavefunction, the remainder consists of a superposition of indistinguishable terms, so that arguably "collapse" of the wavefunction is irrelevant, and the "many worlds" of Everett's interpretation are unified into one. Finally, the analysis suggests a "cosmological interpretation" of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the observer's inability to self-locate in this collection.

quant-ph↗
arXiv2012

Casimir-Polder repulsion: Polarizable atoms, cylinders, spheres, and ellipsoids

Recently, the topic of Casimir repulsion has received a great deal of attention, largely because of the possibility of technological application. The general subject has a long history, going back to the self-repulsion of a conducting spherical shell and the repulsion between a perfect electric conductor and a perfect magnetic conductor. Recently it has been observed that repulsion can be achieved between ordinary conducting bodies, provided sufficient anisotropy is present. For example, an anisotropic polarizable atom can be repelled near an aperture in a conducting plate. Here we provide new examples of this effect, including the repulsion on such an atom moving on a trajectory nonintersecting a conducting cylinder; in contrast, such repulsion does not occur outside a sphere. Classically, repulsion does occur between a conducting ellipsoid placed in a uniform electric field and an electric dipole. The Casimir-Polder force between an anisotropic atom and an anisotropic dielectric semispace does not exhibit repulsion. The general systematics of repulsion are becoming clear.

hep-th↗
arXiv2012

Ordinary versus PT-symmetric $ϕ^3$ quantum field theory

A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric $igϕ^3$ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian $H=p^2+ix^3$, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization-group properties of a conventional Hermitian $gϕ^3$ quantum field theory with those of the PT-symmetric $igϕ^3$ quantum field theory. It is shown that while the conventional $gϕ^3$ theory in $d=6$ dimensions is asymptotically free, the $igϕ^3$ theory is like a $gϕ^4$ theory in $d=4$ dimensions; it is energetically stable, perturbatively renormalizable, and trivial.

hep-th↗
arXiv2012

Stochastic potential and quantum decoherence of heavy quarkonium in the quark-gluon plasma

We propose an open quantum systems approach to the physics of heavy quarkonia in a thermal medium, based on stochastic quantum evolution. This description emphasizes the importance of collisions with the environment and focuses on the concept of spatial decoherence of the heavy quarkonium wave function. It is shown how to determine the parameters of the dynamical evolution, i.e. the real potential and the noise strength, from a comparison with quantities to be obtained from lattice QCD. Furthermore the imaginary part of the lattice QCD heavy quark potential is found to be naturally related to the strength of the noise correlations. We discuss the time evolution of $Q\bar{Q}$ analytically in a limiting scenario for the spatial decoherence and provide a qualitative 1-dimensional numerical simulation of the real-time dynamics.

hep-ph↗
arXiv2012

How unitary cosmology generalizes thermodynamics and solves the inflationary entropy problem

We analyze cosmology assuming unitary quantum mechanics, using a tripartite partition into system, observer and environment degrees of freedom. This generalizes the second law of thermodynamics to "The system's entropy can't decrease unless it interacts with the observer, and it can't increase unless it interacts with the environment." The former follows from the quantum Bayes Theorem we derive. We show that because of the long-range entanglement created by cosmological inflation, the cosmic entropy decreases exponentially rather than linearly with the number of bits of information observed, so that a given observer can reduce entropy by much more than the amount of information her brain can store. Indeed, we argue that as long as inflation has occurred in a non-negligible fraction of the volume, almost all sentient observers will find themselves in a post-inflationary low-entropy Hubble volume, and we humans have no reason to be surprised that we do so as well, which solves the so-called inflationary entropy problem. An arguably worse problem for unitary cosmology involves gamma-ray-burst constraints on the "Big Snap", a fourth cosmic doomsday scenario alongside the "Big Crunch", "Big Chill" and "Big Rip", where an increasingly granular nature of expanding space modifies our life-supporting laws of physics. Our tripartite framework also clarifies when it is valid to make the popular quantum gravity approximation that the Einstein tensor equals the quantum expectation value of the stress-energy tensor, and how problems with recent attempts to explain dark energy as gravitational backreaction from super-horizon scale fluctuations can be understood as a failure of this approximation.

hep-th↗
arXiv2012

Functional RG flow of the effective Hamiltonian action

After a brief review of the definition and properties of the quantum effective Hamiltonian action we describe its renormalization flow by a functional RG equation. This equation can be used for a non-perturbative quantization and study also of theories with bare Hamiltonians which are not quadratic in the momenta. As an example the vacuum energy and gap of quantum mechanical models are computed. Extensions of this framework to quantum field theories are discussed. In particular one possible Lorentz covariant approach for simple scalar field theories is developed. Fermionic degrees of freedom, being naturally described by a first order formulation, can be easily accommodated in this approach.

hep-th↗
arXiv2012

Noncommutativity in (2+1)-dimensions and the Lorentz group

In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible representation of the Lorentz group. The Hilbert space gets the structure of a direct product with the representation space, where we are able to construct operators which realize the algebra of Lorentz transformations. We study the modified Landau problem for both Schrödinger and Dirac particles, whose Hamiltonians are obtained through a kind of non-Abelian Bopp's shift of the dynamical variables from the ones of the usual problem in the normal space. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters. We find no constraint between the parameters referring to no-commutativity in coordinates and momenta but they rather play similar roles. Since the representation space of the unitary irreducible representations SL(2,R) can be realized in terms of spaces of square-integrable functions, we conclude that these models are equivalent to quantum mechanical models of particles living in a space with an additional compact dimension.

hep-th↗
arXiv2011

Trace formula for dielectric cavities II: Regular, pseudo-integrable, and chaotic examples

Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [PRE, vol. 78, 056202 (2008)] the trace formula for both the smooth and the oscillating parts of the resonance density was proposed and checked for the circular cavity. The present paper deals with numerous shapes which would be integrable (square, rectangle, and ellipse), pseudo-integrable (pentagon) and chaotic (stadium), if the cavities were closed (billiard case). A good agreement is found between the theoretical predictions, the numerical simulations, and experiments based on organic micro-lasers.

physics.optics↗
arXiv2011

Poincare recurrence and intermittent loss of quantum Kelvin wave cascades in quantum turbulence

The evolution of the ground state wave function of a zero-temperature Bose-Einstein condensate (BEC) is well described by the Hamiltonian Gross-Pitaevskii (GP) equation. Using a set of appropriately interleaved unitary collision-streaming operators, a quantum lattice gas algorithm is devised which on taking moments recovers the Gross-Pitaevskii (GP) equation in diffusion ordering (time scales as square of length). Unexpectedly, there is a class of initial conditions in which their Poincare recurrence is extremely short. Further it is shown that the Poincare recurrence time scales with diffusion ordering as the the grid is increased. The spectral results of Yepez et.al. [1] for quantum turbulence are corrected and it is found that it is the compressible kinetic energy spectrum that exhibits the 3 cascade regions: a small k classical Kolmogorov k^(-5/3) spectrum, a steep semi-classical cascade region, and a large k quantum Kelvin wave cascade k^(-3) spectrum. The incompressible kinetic energy spectrum exhibits basically a single cascade power law of k^(-3). For winding number 1 linear vortices it is also shown that there is an intermittent loss of Kelvin wave cascade with its signature seen in the time evolution of the kinetic energy, the loss of the k^(-3) spectrum in the incompressible kinetic energy spectrum as well as the minimization of the vortex core isosurfaces that inhibits the Kelvin wave cascade.

quant-ph↗
arXiv2010

Thermalization of Interacting Fermions and Delocalization in Fock space

By means of exact diagonalization, we investigate the onset of 'eigenstate thermalization' and the crossover to ergodicity in a system of 1D fermions with increasing interaction. We show that the fluctuations in the expectation values of the momentum distribution from eigenstate to eigenstate decrease with increasing coupling strength and system size. It turns out that these fluctuations are proportional to the inverse participation ratio of eigenstates represented in the Fock basis. We demonstrate that eigenstate thermalization should set in even for vanishingly small perturbations in the thermodynamic limit.

cond-mat.stat-mech↗
arXiv2012

Efficient estimation of energy transfer efficiency in light-harvesting complexes

The fundamental physical mechanisms of energy transfer in photosynthetic complexes is not yet fully understood. In particular, the degree of efficiency or sensitivity of these systems for energy transfer is not known given their non-perturbative and non-Markovian interactions with proteins backbone and surrounding photonic and phononic environments. One major problem in studying light-harvesting complexes has been the lack of an efficient method for simulation of their dynamics in biological environments. To this end, here we revisit the second-order time-convolution (TC2) master equation and examine its reliability beyond extreme Markovian and perturbative limits. In particular, we present a derivation of TC2 without making the usual weak system-bath coupling assumption. Using this equation, we explore the long time behaviour of exciton dynamics of Fenna-Matthews-Olson (FMO) protein complex. Moreover, we introduce a constructive error analysis to estimate the accuracy of TC2 equation in calculating energy transfer efficiency, exhibiting reliable performance for environments with weak and intermediate memory and strength. Furthermore, we numerically show that energy transfer efficiency is optimal and robust for the FMO protein complex of green sulphur bacteria with respect to variations in reorganization energy and bath correlation time-scales.

quant-ph↗
arXiv2013

Scattering of quantum wave packets by shallow potential islands: A quantum lens

We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing) of light rays by a thin optical lens: Quantum interference between straight paths yields the same lens equation as for refracted rays in classical optics.

quant-ph↗
arXiv2013

Decoherence, relaxation and chaos in a kicked-spin ensemble

We study the dynamics of a quantum spin ensemble controlled by trains of ultrashort pulses. To model disturbances of the kicks, we consider that the spins are submitted to different kick trains which follow regular, random, stochastic or chaotic dynamical processes. These are described by dynamical systems on a torus. We study the quantum decoherence and the population relaxation of the spin ensemble induced by these classical dynamical processes disturbing the kick trains. For chaotic kick trains we show that the decoherence and the relaxation processes exhibit a signature of chaos directly related to the Lyapunov exponents of the dynamical system. This signature is a horizon of coherence, i.e. a preliminary duration without decoherence followed by a rapid decoherence process.

quant-ph↗
arXiv2011

Activation of Non-Local Quantum Resources

We find two two-qubit states such that any number of copies of one state or the other cannot violate the CHSH Bell inequality. However, their tensor product can produce a CHSH violation of at least 2.023. We also identify a CHSH-local state such that two copies of it are CHSH-violating. The tools employed here can be easily adapted to find instances of non-locality activation in arbitrary Bell scenarios.

quant-ph↗
arXiv2010

Demonstration of a Tuneable Coupler for Superconducting Qubits Using Coherent, Time Domain, Two-Qubit Operations

A major challenge in the field of quantum computing is the construction of scalable qubit coupling architectures. Here, we demonstrate a novel tuneable coupling circuit that allows superconducting qubits to be coupled over long distances. We show that the inter-qubit coupling strength can be arbitrarily tuned over nanosecond timescales within a sequence that mimics actual use in an algorithm. The coupler has a measured on/off ratio of 1000. The design is self-contained and physically separate from the qubits, allowing the coupler to be used as a module to connect a variety of elements such as qubits, resonators, amplifiers, and readout circuitry over long distances. Such design flexibility is likely to be essential for a scalable quantum computer.

quant-ph↗