Excited state quantum phase transitions in many-body systems

Phenomena analogous to ground state quantum phase transitions have recently been noted to occur among states throughout the excitation spectra of certain many-body models. These excited state phase transitions are manifested as simultaneous singularities in the eigenvalue spectrum (including the gap or level density), order parameters, and wave function properties. In this article, the characteristics of excited state quantum phase transitions are investigated. The finite-size scaling behavior is determined at the mean-field level. It is found that excited state quantum phase transitions are universal to two-level bosonic and fermionic models with pairing interactions.     

Spacetime path formalism for massive particles of any spin

Earlier work presented spacetime path formalism for relativistic quantum mechanics arising naturally from the fundamental principles of the Born probability rule, superposition, and spacetime translation invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches to relativistic quantum mechanics in the literature. Because time is treated similarly to the three-space coordinates, rather than as an evolution parameter, such approaches have proved particularly useful in the study of quantum gravity and cosmology. The present paper extends the foundational spacetime path formalism to include massive, non-scalar particles of any (integer or half-integer) spin. This is done by generalizing the principle of translational invariance used in the scalar case to the principle of full Poincaré invariance, leading to a formulation for the non-scalar propagator in terms of a path integral over the Poincaré group. Once the difficulty of the non-compactness of the component Lorentz group is dealt with, the subsequent development is remarkably parallel to the scalar case. This allows the formalism to retain a clear probabilistic interpretation throughout, with a natural reduction to non-relativistic quantum mechanics closely related to the well-known generalized Foldy-Wouthuysen transformation.     

Relativistic quantum particle in a homogeneous external field

The model of the relativistic quantum particle in a homogeneous external field is proposed. This model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space in our case is the one-dimensional Lobachevsky space. We have found the wave functions and propagator for the model under study in both x- and p-representations.     

Relativistic optics in gravitational lensing: The focus of a cluster and its aberrations

In this article, general idea of focusing is studied within the framework of optics extension into general relativity (covariant optics). In a configuration of static spacetime, the general, mathematically rigorous treatment of rays, wavefronts and caustics of spherical symmetry is presented, particularly with regard to problems of obtaining them within general relativity. An original result is the aberration formulation to covariant optics, whose application is given in this paper; a particular solution of Einstein equations is finally chosen to provide concrete, exact results of cluster focal length and its aberration structure. In this way, a gravitational lensing situation is shown to be a true lens.     

Energy exchange in heterogeneous cumulative mediums induced by nonstationary quantum flux

It is known that energy flux from nonstationary source is able to modulate the energy exchange in the heterogeneous cumulative medium in the quantum optics approximation. This paper presents the results of further investigation of energy exchange problem in the heterogeneous medium with cumulative features. Equation for dynamics of dispersion term is derived and relative contribution of dissipative and dispersion term is estimated. The possibility of the expansion of nonstationary solution of energy exchange equation into basis of corresponding stationary solutions (dissipative structures) is shown. The physical interpretation of obtained results in terms of the dissipative structure variations is given.     

Physical defects in fiber optics: A theoretical framework in phase space

A Gaussian symplectic map is used to obtain the Wigner distribution function (WDF) of an optical fiber sectioned by a media with different refractive index. It is found that the WDF after the defect is simply the original Gaussian corrected by a polynomial term.     

The Aharonov-Bohm effect in the momentum space

The Schrödinger formalism of quantum mechanics is used to demonstrate the existence of the Aharonov-Bohm effect in momentum space and set-ups for experimentally demonstrating it are proposed for either free or ballistic electrons.     

Admissible states in quantum phase space

We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a formula for the momentum correlations of arbitrary order and derive explicit expressions for the wave functions in terms of time-dependent and independent Wigner functions. We show that the pure state quantum condition is preserved by the Moyal (but not by the classical Liouville) time evolution and is consistent with a generic stargenvalue equation. As a by-product Baker's converse construction is generalized both to an arbitrary stargenvalue equation, associated to a generic phase space symbol, as well as to the time-dependent case. These results are properly extended to the mixed state quantum condition, which is proved to imply the Heisenberg uncertainty relations. Globally, this formalism yields the complete characterization of the kinematical structure of Wigner quantum mechanics. The previous results are then succinctly generalized for various quasi-distributions. Finally, the formalism is illustrated through the simple examples of the harmonic oscillator and the free Gaussian wave packet. As a by-product, we obtain in the former example an integral representation of the Hermite polynomials.     

Newton-Leibniz integration for ket-bra operators in quantum mechanics (V)—Deriving normally ordered bivariate-normal-distribution form of density operators and developing their phase space formalism

We show that Newton-Leibniz integration over Dirac’s ket-bra projection operators with continuum variables, which can be performed by the technique of integration within ordered product (IWOP) of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480], can directly recast density operators and generalized Wigner operators into normally ordered bivariate-normal-distribution form, which has resemblance in statistics. In this way the phase space formalism of quantum mechanics can be developed. The Husimi operator, entangled Husimi operator and entangled Wigner operator for entangled particles with different masses are naturally introduced by virtue of the IWOP technique, and their physical meanings are explained.     

Relativistic effects in quantum walks: Klein's paradox and zitterbewegung

Quantum walks are not only algorithmic tools for quantum computation but also non-trivial models describing various physical processes. The Letter compares one-dimensional version of the free particle Dirac equation with the discrete time quantum walk (DTQW). It is shown that two relativistic effects associated with the Dirac equation, namely zitterbewegung (quivering motion) and Klein's paradox, are manifested in DTQW. A special case of DTQW for Lorentz invariance not satisfied in the corresponding continuous limit is considered. The effects are examined.     

Quantum strategies in moving frames

We investigate quantum strategies in moving frames by considering Prisoners' Dilemma and propose four thresholds of γ for two players to determine their Nash Equilibria. We find that the relativistic operations could enhance or diminish the quantum features of the game for different players who move in different directions relative to the arbiter.     

Standard and non-standard metarefraction with confocal lenslet arrays

A recent paper demonstrated that two lenslet arrays with focal lengths f₁ and f₂, separated by f₁+f₂, change the direction of transmitted light rays approximately like the interface between isotropic media with refractive indices n₁ and n₂, where n₁/n₂=-f₁/f₂ [J. Courtial, New J. Phys. 10 (2008) 083033]. This is true if light passes through corresponding lenslets, that is lenslets that share an optical axis. Light can also pass through different combinations of non-corresponding lenslets. Such light can be either absorbed or allowed to form “ghost images”; either way, it leads to a limitation of the field of view of confocal lenslet arrays. This paper describes, qualitatively and quantitatively, a number of such field-of-view limitations.     

Another derivation of Weinberg's formula

To investigate how quantum effects might modify special relativity, we will study a Lorentz transformation between classical and quantum reference frames and express it in terms of the four-dimensional (4D) momentum of the quantum reference frame. The transition from the classical expression of the Lorentz transformation to a quantum-mechanical one requires us to symmetrize the expression and replace all its dynamical variables with the corresponding operators, from which we can obtain the same conclusion as that from quantum field theory (given by Weinberg's formula): owing to the Heisenberg's uncertainty relation, a particle (as a quantum reference frame) can propagate over a spacelike interval.     

Geometric limits to geometric optical imaging with infinite, planar, non-absorbing sheets

Wave optics can limit the ways in which optical components can change light-ray fields. Optical components called METATOYs trade in the continuity of the phase fronts and the precision to which they change light-ray fields in return for additional possibilities when changing light-ray fields. Now only geometry limits the possible mappings between the positions of an object and its geometric image. Here, I study such limitations for the case of an infinite, planar, non-absorbing sheet that images the entire three-dimensional space. The most general case of such a sheet is equivalent to a thin lens with different object- and image-sided focal lengths. Special cases include ordinary thin lenses, confocal lenslet arrays, and negative refration with n₂=-n₁.     

Quantum mechanics of Klein-Gordon-type fields and quantum cosmology

With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂_t²+D)ψ(t)=0, where and D is a positive-definite operator acting in a Hilbert space . In particular, we determine all the positive-definite inner products on the space of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in . Among these is a particular choice that generates t-translations in and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in , and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in , show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the dynamics. Our method is based on the central postulates of nonrelativistic quantum mechanics, especially the quest for a genuine probabilistic interpretation and a unitary Schrödinger time-evolution. It generalizes to arbitrary minisuperspace (spatially homogeneous) models and provides a way of unifying the two main approaches to the canonical quantum cosmology based on these models, namely quantization before and after imposing the Hamiltonian constraint.     

Equiangular-spiral bent lightpipes with arbitrary bent angle

A recent study proposed the concept of a leakage-free bent lightpipe with an equiangular-spiral shape [S.-C. Chu, J.-L. Chern, Opt. Lett. 30 (2005) 3006]. This paper extends the design of a leakage-free equiangular-spiral bent lightpipe with arbitrary-bend-angle and addresses in detail the mathematical formalism required to build such an equiangular-spiral bent lightpipe. Furthermore, a comparison of the proposed equiangular-spiral bent lightpipe and a conventional circular bent lightpipe is provided. Numerical verifications are discussed, and experimental explorations with different bent shapes and angles are carried out for comparison. Results show that equiangular-spiral bent lightpipes with different bent angles exhibit a theoretical 100% transmission with more than 76% efficiency when practically propagating, which is much better than conventional circular bent lightpipes. The output irradiance distributions of bent lightpipes with different bent shapes are also investigated.     

Refining a relativistic,hydrodynamic solver: Admitting ultra-relativistic flows

We have undertaken the simulation of hydrodynamic flows with bulk Lorentz factors in the range 10²–10⁶. We discuss the application of an existing relativistic, hydrodynamic primitive variable recovery algorithm to a study of pulsar winds, and, in particular, the refinement made to admit such ultra-relativistic flows. We show that an iterative quartic root finder breaks down for Lorentz factors above 10² and employ an analytic root finder as a solution. We find that the former, which is known to be robust for Lorentz factors up to at least 50, offers a 24% speed advantage. We demonstrate the existence of a simple diagnostic allowing for a hybrid primitives recovery algorithm that includes an automatic, real-time toggle between the iterative and analytical methods. We further determine the accuracy of the iterative and hybrid algorithms for a comprehensive selection of input parameters and demonstrate the latter’s capability to elucidate the internal structure of ultra-relativistic plasmas. In particular, we discuss simulations showing that the interaction of a light, ultra-relativistic pulsar wind with a slow, dense ambient medium can give rise to asymmetry reminiscent of the Guitar nebula leading to the formation of a relativistic backflow harboring a series of internal shockwaves. The shockwaves provide thermalized energy that is available for the continued inflation of the PWN bubble. In turn, the bubble enhances the asymmetry, thereby providing positive feedback to the backflow.     

The laser-dressed potential binding energy of a hydrogenic impurity in a spherical quantum dot by the analytical transfer matrix method

The analytical transfer matrix method (ATMM) is efficient and accurate for understanding the nature of bound states. In this paper, it is applied to obtain the binding energy of a hydrogenic impurity placed at the center of the spherical quantum dots (QDs) in an intense laser field. Our results agree with the exact energies in Varshni [Superlattices Microstructures 30 (2001) 45]. Therefore, ATMM gives us an alternative approach to tackle the problem of impurities placed in nano-structures under intense laser fields.