1,208 research outputs found
Hamiltonian formulation of nonequilibrium quantum dynamics: geometric structure of the BBGKY hierarchy
Time-resolved measurement techniques are opening a window on nonequilibrium
quantum phenomena that is radically different from the traditional picture in
the frequency domain. The simulation and interpretation of nonequilibrium
dynamics is a conspicuous challenge for theory. This paper presents a novel
approach to quantum many-body dynamics that is based on a Hamiltonian
formulation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of
equations of motion for reduced density matrices. These equations have an
underlying symplectic structure, and we write them in the form of the classical
Hamilton equations for canonically conjugate variables. Applying canonical
perturbation theory or the Krylov-Bogoliubov averaging method to the resulting
equations yields a systematic approximation scheme. The possibility of using
memory-dependent functional approximations to close the Hamilton equations at a
particular level of the hierarchy is discussed. The geometric structure of the
equations gives rise to reduced geometric phases that are observable even for
noncyclic evolutions of the many-body state. The formalism is applied to a
finite Hubbard chain which undergoes a quench in on-site interaction energy U.
Canonical perturbation theory, carried out to second order, fully captures the
nontrivial real-time dynamics of the model, including resonance phenomena and
the coupling of fast and slow variables.Comment: 17 pages, revise
Appell Transformation and Canonical Transforms
The interpretation of the optical Appell transformation, as previously elaborated in relation to the free-space paraxial propagation under both a rectangular and a circular cylindrical symmetry, is reviewed. Then, the caloric Appell transformation, well known in the theory of heat equation, is shown to be amenable for a similar interpretation involving the Laplace transform rather than the Fourier transform, when dealing with the 1D heat equation. Accordingly, when considering the radial heat equation, suitably defined Hankel-type transforms come to be involved in the inherent Appell transformation. The analysis is aimed at outlining the link between the Appell transformation and the canonical transforms
Bi-Orthogonal Approach to Non-Hermitian Hamiltonians with the Oscillator Spectrum: Generalized Coherent States for Nonlinear Algebras
A set of Hamiltonians that are not self-adjoint but have the spectrum of the
harmonic oscillator is studied. The eigenvectors of these operators and those
of their Hermitian conjugates form a bi-orthogonal system that provides a
mathematical procedure to satisfy the superposition principle. In this form the
non-Hermitian oscillators can be studied in much the same way as in the
Hermitian approaches. Two different nonlinear algebras generated by properly
constructed ladder operators are found and the corresponding generalized
coherent states are obtained. The non-Hermitian oscillators can be steered to
the conventional one by the appropriate selection of parameters. In such limit,
the generators of the nonlinear algebras converge to generalized ladder
operators that would represent either intensity-dependent interactions or
multi-photon processes if the oscillator is associated with single mode photon
fields in nonlinear media.Comment: this abridged version (37 pages, 11 figures) includes simplified
formulae and correction of misprint
A Survey of Signal Processing Problems and Tools in Holographic Three-Dimensional Television
Cataloged from PDF version of article.Diffraction and holography are fertile areas for application of signal theory and processing. Recent work on 3DTV displays has posed particularly challenging signal processing problems. Various procedures to compute Rayleigh-Sommerfeld, Fresnel and Fraunhofer diffraction exist in the literature. Diffraction between parallel planes and tilted planes can be efficiently computed. Discretization and quantization of diffraction fields yield interesting theoretical and practical results, and allow efficient schemes compared to commonly used Nyquist sampling. The literature on computer-generated holography provides a good resource for holographic 3DTV related issues. Fast algorithms to compute Fourier, Walsh-Hadamard, fractional Fourier, linear canonical, Fresnel, and wavelet transforms, as well as optimization-based techniques such as best orthogonal basis, matching pursuit, basis pursuit etc., are especially relevant signal processing techniques for wave propagation, diffraction, holography, and related problems. Atomic decompositions, multiresolution techniques, Gabor functions, and Wigner distributions are among the signal processing techniques which have or may be applied to problems in optics. Research aimed at solving such problems at the intersection of wave optics and signal processing promises not only to facilitate the development of 3DTV systems, but also to contribute to fundamental advances in optics and signal processing theory. © 2007 IEEE
Charged Particle Optics Theory
Charged Particle Optics Theory: An Introduction identifies the most important concepts of charged particle optics theory, and derives each mathematically from the first principles of physics. Assuming an advanced undergraduate-level understanding of calculus, this book follows a logical progression, with each concept building upon the preceding one. Beginning with a non-mathematical survey of the optical nature of a charged particle beam, the text: Discusses both geometrical and wave optics, as well as the correspondence between them Describes the two-body scattering problem, which is essential to the interaction of a fast charged particle with matter Introduces electron emission as a practical consequence of quantum mechanics Addresses the Fourier transform and the linear second-order differential equation Includes problems to amplify and fill in the theoretical details, with solutions presented separately Charged Particle Optics Theory: An Introduction makes an ideal textbook as well as a convenient reference on the theoretical origins of the optics of charged particle beams. It is intended to prepare the reader to understand the large body of published research in this mature field, with the end result translated immediately to practical application
Two Mathematically Equivalent Versions of Maxwell's Equations
This paper is a review of the canonical proper-time approach to relativistic
mechanics and classical electrodynamics. The purpose is to provide a physically
complete classical background for a new approach to relativistic quantum
theory. Here, we first show that there are two versions of Maxwell's equations.
The new version fixes the clock of the field source for all inertial observers.
However now, the (natural definition of the effective) speed of light is no
longer an invariant for all observers, but depends on the motion of the source.
This approach allows us to account for radiation reaction without the
Lorentz-Dirac equation, self-energy (divergence), advanced potentials or any
assumptions about the structure of the source. The theory provides a new
invariance group which, in general, is a nonlinear and nonlocal representation
of the Lorentz group. This approach also provides a natural (and unique)
definition of simultaneity for all observers. The corresponding particle theory
is independent of particle number, noninvariant under time reversal (arrow of
time), compatible with quantum mechanics and has a corresponding positive
definite canonical Hamiltonian associated with the clock of the source.
We also provide a brief review of our work on the foundational aspects of the
corresponding relativistic quantum theory. Here, we show that the standard
square-root and the Dirac equations are actually two distinct
spin- particle equations.Comment: Appeared: Foundations of Physic
Quantum Information Propagation Preserving Computational Electromagnetics
We propose a new methodology, called numerical canonical quantization, to
solve quantum Maxwell's equations useful for mathematical modeling of quantum
optics physics, and numerical experiments on arbitrary passive and lossless
quantum-optical systems. It is based on: (1) the macroscopic (phenomenological)
electromagnetic theory on quantum electrodynamics (QED), and (2) concepts
borrowed from computational electromagnetics. It was shown that canonical
quantization in inhomogeneous dielectric media required definite and proper
normal modes. Here, instead of ad-hoc analytic normal modes, we numerically
construct complete and time-reversible normal modes in the form of traveling
waves to diagonalize the Hamiltonian. Specifically, we directly solve the
Helmholtz wave equations for a general linear, reciprocal, isotropic,
non-dispersive, and inhomogeneous dielectric media by using either
finite-element or finite-difference methods. To convert a scattering problem
with infinite number of modes into one with a finite number of modes, we impose
Bloch-periodic boundary conditions. This will sparsely sample the normal modes
with numerical Bloch-Floquet-like normal modes. Subsequent procedure of
numerical canonical quantization is straightforward using linear algebra. We
provide relevant numerical recipes in detail and show an important numerical
example of indistinguishable two-photon interference in quantum beam splitters,
exhibiting Hong-Ou-Mandel effect, which is purely a quantum effect. Also, the
present methodology provides a way of numerically investigating existing or new
macroscopic QED theories. It will eventually allow quantum-optical numerical
experiments of high fidelity to replace many real experiments as in classical
electromagnetics.Comment: 17 pages, 11 figures, journal article submitted to Physical review A
(under review
Exact Solution for A Real Polaritonic System Under Vibrational Strong Coupling in Thermodynamic Equilibrium: Absence of Zero Temperature and Loss of Light-Matter Entanglement
The first exact quantum simulation of a real molecular system (HD+) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled systems of mixed quantum statistics (Bosons and Fermions) are discussed and circumvented by the specific choice of our molecular system. Our exact simulations reveal the absence of a zero temperature for the strongly coupled matter and light subsystems, due to cavity induced non-equilibrium conditions. Furthermore, we explore the temperature dependency of light-matter quantum entanglement, which emerges for the groundstate, but is quickly lost already in the deep cryogenic regime, opposing predictions from phenomenological models (Jaynes-Cummings). Distillable molecular light-matter entanglement of ro-vibrational states may open interesting perspectives for quantum technological applications. Moreover, we find that the dynamics (fluctuations) of matter remains modified by the quantum nature of the thermal and vacuum field fluctuations for significant temperatures, e.g. at ambient conditions. These observations (loss of entanglement and coupling to quantum fluctuations) has far reaching consequences for the understanding and control of polaritonic chemistry and materials science, since a semi-classical theoretical description of light-matter interaction becomes feasible, but the typical canonical equilibrium assumption for the nuclear dynamics remains broken. This opens the door for quantum fluctuations induced stochastic resonance phenomena under vibrational strong coupling. A plausible theoretical mechanism to explain the experimentally observed resonance phenomena in absence of periodic driving, which have not yet been understood
- …