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Introducing a quantum kinetic model using the generalized Boltzmann equation in the complex phase space
摘要： In the present work, using the generalized Boltzmann equation of the ?rst author [Phys. Rev. E 94, 023316 (2016)], a quantum kinetic model in the complex phase space is proposed. Employing the Chapman-Enskog analysis and applying the Wick rotation (using complex-valued relaxation time), it is shown that the present model recovers the time-dependent Schr?edinger equation, while preserving the main features of the conventional lattice Boltzmann models, e.g., simplicity of implementation, second-order accuracy (in space), and convenience in parallel programming. The present results are numerically veri?ed by simulating three benchmark problems.
关键词： quantum kinetic model,Schr?dinger equation,Wick rotation,lattice Boltzmann models,generalized Boltzmann equation,Chapman-Enskog analysis,complex phase space
更新于2025-09-23 15:21:21
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Beam frame representation for ultra-wide-band radiation from volume source distributions: Frequency domain and time domain formulations
摘要： We present two novel beam summation (BS) schemes for radiation from time-harmonic or time-dependent volume source distributions, where the field is expanded using a discrete phase-space set of beam-wave propagators. The generic term “beams” is used here for both the frequency-domain and the time-domain formulations where the propagators are iso-diffracting Gaussian beam (ID-GB) or iso-diffracting pulsed beams (ID-PB), respectively. The formulations are structured upon the recently formulated “beam-frame” theorem that establishes these phase-space beam-sets as frame-sets everywhere in the propagation domain, and not only over the aperture plane as in previous formulations. The expansion coefficients are obtained by projecting the source distributions over the dual beam-frame sets that have essentially the same structure as the basic sets. As such, these formulations constitute local generalization to the conventional plane-waves or Green’s function formulations, and also reduce the overall degrees of freedom needed to describe the radiated field. As demonstrated by the numerical examples they resolve the local features of the source distributions in space-time, and hence provide a basis for a new local inverse scattering theory to be presented subsequently.
关键词： beam summation methods,pulsed beams,Gaussian beams,phase space representations,ultra wide band,time domain,Radiation theory
更新于2025-09-23 15:21:21
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Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance
摘要： It is often said that measuring a system’s position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a “weak-measurement”, this disturbance can be reduced. One might expect this comes at the cost of also reducing the measurement’s precision. However, it was recently demonstrated that a sequence consisting of a weak position measurement followed by a regular momentum measurement can probe a quantum system at a single point, with zero width, in position-momentum space. Here, we study this “joint weak-measurement” and reconcile its compatibility with the uncertainty principle. While a single trial probes the system with a resolution that can saturate Heisenberg’s limit, we show that averaging over many trials can be used to surpass this limit. The weak-measurement does not trade-away precision, but rather another type of uncertainty called “predictability” which quantifies the certainty of retrodicting the measurement’s outcome.
关键词： weak-measurement,Heisenberg uncertainty principle,phase space,predictability,quantum measurement
更新于2025-09-23 15:21:01
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Wehrl entropy based quantification of nonclassicality for single mode quantum optical states
摘要： Nonclassical states of a quantized light are described in terms of Glauber-Sudarshan P distribution which is not a genuine classical probability distribution. Despite several attempts, defining a uniform measure of nonclassicality (NC) for the single mode quantum states of light is yet an open task. In our previous work [Phys. Rev. A 95, 012330 (2017)] we have shown that the existing well-known measures fail to quantify the NC of single mode states that are generated under multiple NC-inducing operations. In this paper, we propose a new quantification of NC for the single mode quantum states as the difference between the total Wehrl entropy of the state and the maximum Wehrl entropy arising due to its classical characteristics. The classical reference state is chosen at the same randomness, given by the von-Neumann entropy, as the state itself. We further suggest operational interpretation of the proposed measure in terms of phase-space sampling entropy as well as potential to generate entanglement, in the case of pure states. We obtain analytic expressions of NC for pure states and Gaussian mixed states. We show that, along with the states generated under single NC-inducing operations, also for the broader class of states that are generated under multiple NC-inducing operations, our quantification enumerates the NC consistently. However, the evaluation of NC for the non-Gaussian mixed states is subject to extensive numerical computation that lies beyond the scope of the current work. We finally conclude with certain open questions.
关键词： Wehrl Entropy,Quantumness,Phase Space Distributions,Quantum Optics,Nonclassicality
更新于2025-09-23 15:21:01
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Design of Nonparaxial Accelerating Beams Based on Wigner Distribution Function
摘要： Design of nonparaxial accelerating beams based on Wigner distribution function. Accelerating beams, which propagate along curved trajectories in free space, have been widely applied to generate various two-dimensional convex and nonconvex caustic beams in paraxial and nonparaxial regimes. Recently, it is found that the design of accelerating beams in phase space is more informative and also enables construction of some three-dimensional accelerating beams. However, the proposed Wigner distribution function (WDF) method is still limited to the paraxial case in constructing accelerating beams. In this work, we investigate the phase-space design of accelerating beams in the nonparaxial regime with a new form of the constructed WDF. With this method, both the initial light field distribution in real space and angular spectrum in Fourier space of the accelerating beam propagating along a desired nonparaxial trajectory can be obtained simultaneously. To confirm this idea, a few types of different accelerating beams such as circular beams and parabola beams have been constructed for demonstration. The approach is expected to pave the way in designing more highly tailored accelerating beams in different scenarios and thus facilitate a variety of applications.
关键词： Wigner distribution function,caustic beams,nonparaxial accelerating beams,phase-space design
更新于2025-09-16 10:30:52
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Three-dimensional classical imaging of a pattern localized in a phase space
摘要： In most imaging experiments, the structure of an object is defined in a position space. Such a structural pattern can be stationary, or for a dynamic object it can be nonstationary with time. An image of such an optically responsive object can be produced with a lens, therefore such an object can be seen with a camera or by the human eye. In this paper, we go beyond the conventional notion of imaging. A structural pattern of objects in our experiment is defined in a phase space, therefore such a pattern cannot be imaged with a lens or a camera, and the human eye cannot visualize it. A pattern in phase space is produced from object transparencies and imprinted onto the phase space of an atomic gaseous medium of a Doppler-broadened absorption profile at room temperature by utilizing velocity-selective hole burning in the absorption profile. The pattern is localized in a unique three-dimensional phase space, which is a subspace of the six-dimensional phase space. Tomographic images of the localized phase-space pattern are captured at different momentum locations by a laser light that has never interacted with actual objects. In addition, imaging of an imprinted phase-space pattern of an object of nonuniform transmittance is presented.
关键词： imaging,tomographic imaging,phase space,Doppler-broadened absorption profile,velocity-selective hole burning
更新于2025-09-10 09:29:36
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[IEEE 2018 25th IEEE International Conference on Image Processing (ICIP) - Athens, Greece (2018.10.7-2018.10.10)] 2018 25th IEEE International Conference on Image Processing (ICIP) - Fast Non-Linear Methods for Dynamic Texture Prediction
摘要： This paper aims to develop a fast dynamic-texture prediction method, using tools from non-linear dynamical modeling, and fast approaches for approximate regression. We consider dynamic textures to be described by patch-level non-linear processes, thus requiring tools such as delay-embedding to uncover a phase-space where dynamical evolution can be more easily modeled. After mapping the observed time-series from a dynamic texture video to its recovered phase-space, a time-efficient approximate prediction method is presented which utilizes locality-sensitive hashing approaches to predict possible phase-space vectors, given the current phase-space vector. Our experiments show the favorable performance of the proposed approach, both in terms of prediction fidelity, and computational time. The proposed algorithm is applied to shading prediction in utility scale solar arrays.
关键词： solar energy,shading prediction,dynamic textures,phase-space reconstruction
更新于2025-09-10 09:29:36
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Time-of-flight electron energy loss spectroscopy by longitudinal phase space manipulation with microwave cavities
摘要： The possibility to perform high-resolution time-resolved electron energy loss spectroscopy has the potential to impact a broad range of research fields. Resolving small energy losses with ultrashort electron pulses, however, is an enormous challenge due to the low average brightness of a pulsed beam. In this paper, we propose to use time-of-flight measurements combined with longitudinal phase space manipulation using resonant microwave cavities. This allows for both an accurate detection of energy losses with a high current throughput and efficient monochromation. First, a proof-of-principle experiment is presented, showing that with the incorporation of a compression cavity the flight time resolution can be improved significantly. Then, it is shown through simulations that by adding a cavity-based monochromation technique, a full-width-at-half-maximum energy resolution of 22 meV can be achieved with 3.1 ps pulses at a beam energy of 30 keV with currently available technology. By combining state-of-the-art energy resolutions with a pulsed electron beam, the technique proposed here opens up the way to detecting short-lived excitations within the regime of highly collective physics.
关键词： electron energy loss spectroscopy,longitudinal phase space manipulation,ultrashort electron pulses,time-of-flight,microwave cavities
更新于2025-09-10 09:29:36
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Testing nonclassicality with exact Wigner currents for an anharmonic quantum system
摘要： Phase-space features of the Wigner flow for an anharmonic quantum system driven by the harmonic oscillator potential modified by the addition of an inverse square (one-dimensional Coulomb-like) contribution are analytically described in terms of Wigner functions and Wigner currents. Reporting about three correlated continuity equations which quantify the flux of quantum information in the phase space, the nonclassicality profile of such an anharmonic system can be consistently obtained in terms of the fluxes of probability, purity, and von Neumann–like entropy. Considering that quantum fluctuations can be identified from distortions over the classical regime, they can be quantified through the above-mentioned information fluxes whenever some classically bounded volume of the phase space is selected. Our results suggest that the Wigner flow approach works as a probe of quantumness and classicality for a large set of anharmonic quantum systems driven by quantum wells.
关键词： anharmonic quantum system,Wigner flow,quantum information,phase space,nonclassicality
更新于2025-09-09 09:28:46
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Theory of relaxation oscillations in exciton-polariton condensates
摘要： We provide an analytical and numerical description of relaxation oscillations in the nonresonantly pumped polariton condensate. Presented considerations are based on coupled rate equations that are derived from the open dissipative Gross-Pitaevskii model. The evolution of the condensate density can be explained qualitatively by studying the topology of the trajectory in phase space. We use a ?xed points analysis for the classi?cation of the different regimes of condensate dynamics, including fast stabilization, slow oscillations, and ultrashort pulse emission. We obtain an analytical condition for the occurrence of relaxation oscillations. Continuous and pulsed condensate excitations are considered and we demonstrate that, in the latter case, the existence of the second reservoir is necessary for the emergence of oscillations. We show that relaxation oscillations should be expected to occur in systems with relatively short polariton lifetimes.
关键词： phase space,nonresonantly pumped,relaxation oscillations,fixed points analysis,exciton-polariton condensates,Gross-Pitaevskii model
更新于2025-09-09 09:28:46