arXiv subjects

Mustafa Amin

Publications and source records attributed to Mustafa Amin.

12 recordsLinked to original sources

arXiv2026

Uncertainty and Wigner negativity in Hilbert-space classical mechanics

Classical mechanics, in the Koopman-von Neumann formulation, is described in Hilbert space. It is shown here that classical canonical transformations are generated by Hermitian operators that are in general noncommutative. This naturally brings about uncertainty relations inherent in classical mechanics, for example between position and the generator of space translations, between momentum and the generator of momentum translations, and between dynamical time and the Liouvillian, to name a few. Further, it is shown that the Wigner representation produces a quasi-probability distribution that can take on negative values. Thus, two of the hallmark features of quantum mechanics are reproduced, and become apparent, in a Hilbert-space formulation of classical mechanics.

quant-ph↗

arXiv2025

Solutions of Koopman-von Neumann equations, their superpositions, orthogonality and uncertainties

The Koopman-von Neumann (KvN) formulation brings classical mechanics to Hilbert space, but many techniques familiar from quantum mechanics remain missing. One would hope to solve eigenvalue problems, obtain orthonormal eigenstates of Hermitian operators and ascribe meaning to a coherent superposition of states, among other things. Here we consider the general KvN equation for a classical probability amplitude and show that its so-called gauge freedom allows the separation of variables. The amenability to Hilbert-space methods of the resulting KvN solutions is investigated. We construct superpositions from differently-gauged Liouvillian eigenstates, and find an orthonormal set among them. We find that some separable solutions describe the canonical ensemble with temperature related to the separation constant. Classical uncertainty relations arise naturally in the KvN formalism. We discuss one between the dynamical time and the Liouvillian in terms of the statistical description of classical systems.

quant-ph↗

arXiv2025

Form-preserving transformations of wave and Wigner functions

Solutions of the time-dependent Schr\"odinger equation are mapped to other solutions for a (possibly) different potential by so-called form-preserving transformations. These time-dependent transformations of the space and time coordinates can produce remarkable solutions with surprising properties. A classic example is the force-free accelerating Airy beam found by Berry and Balazs. We review the 1-dimensional form-preserving transformations and show that they also yield Senitzky coherent excited states and the free dispersion of any harmonic-oscillator stationary state. Form preservation of the $D$- and 3-dimensional Schr\"odinger equation with both a scalar and a vector potential is then considered. Time-dependent rotations may be included when a vector potential is present; we find a general transformation formula for this case. Quantum form-preserving maps are also considered in phase space. First, the wave-function transformation is shown to produce a simple result for Wigner functions: they transform as a true phase-space probability would. The explicit transformation formula explains and generalizes the rigid evolution of curves in phase space that characterize the Airy beam and the coherent excited states. Then we recover the known form-preserving transformations from the Moyal equation obeyed by Wigner functions.

quant-ph↗

arXiv2024

Conversations and Deliberations: Non-Standard Cosmological Epochs and Expansion Histories

This document summarizes the discussions which took place during the PITT-PACC Workshop entitled "Non-Standard Cosmological Epochs and Expansion Histories," held in Pittsburgh, Pennsylvania, Sept. 5-7, 2024. Much like the non-standard cosmological epochs that were the subject of these discussions, the format of this workshop was also non-standard. Rather than consisting of a series of talks from participants, with each person presenting their own work, this workshop was instead organized around free-form discussion blocks, with each centered on a different overall theme and guided by a different set of Discussion Leaders. This document is not intended to serve as a comprehensive review of these topics, but rather as an informal record of the discussions that took place during the workshop, in the hope that the content and free-flowing spirit of these discussions may inspire new ideas and research directions.

astro-ph.CO↗

arXiv2022

Deconjugation of canonical variables and the Koopman-von Neumann theory

The Koopman-von Neumann (KvN) theory is one where the dynamical momentum is not canonically conjugate to position, i.e., position and momentum are deconjugated. From this point of view, we show that the KvN theory arises from quantum mechanics, extracting classical equations of motion from quantum ones. However, preserving the canonical structure of the theory requires introducing ``auxiliary'' canonical conjugates to position and momentum. We show that using the KvN formulation to study the interaction between quantum and classical systems forces the auxiliary variables to take on a physical role. While giving rise to classical behaviour, the KvN theory might be more than classical.

quant-ph↗

arXiv2022

Report of the Topical Group on Cosmic Probes of Dark Matter for Snowmass 2021

Cosmological and astrophysical observations currently provide the only robust, positive evidence for dark matter. Cosmic probes of dark matter, which seek to determine the fundamental properties of dark matter through observations of the cosmos, have emerged as a promising means to reveal the nature of dark matter. This report summarizes the current status and future potential of cosmic probes to inform our understanding of the fundamental nature of dark matter in the coming decade.

hep-ph↗

arXiv2022

The Physics of Light Relics

Many well-motivated extensions of the Standard Model predict the existence of new light species that may have been produced in the early universe. Prominent examples include axions, sterile neutrinos, gravitinos, dark photons, and more. The gravitational influence of light relics leaves imprints in the cosmic microwave background fluctuations, the large-scale structure of the universe and the primordial element abundances. In this paper, we detail the physics of cosmological light relics, and describe how measurements of their relic density and mass serve as probes of physics beyond the Standard Model. A measurement of the light relic density at the precision of upcoming cosmological surveys will point the way toward new physics or severely constrain the range of viable extensions to the Standard Model.

hep-ph↗

arXiv2022

Snowmass2021 Cosmic Frontier White Paper: Dark Matter Physics from Halo Measurements

The non-linear process of cosmic structure formation produces gravitationally bound overdensities of dark matter known as halos. The abundances, density profiles, ellipticities, and spins of these halos can be tied to the underlying fundamental particle physics that governs dark matter at microscopic scales. Thus, macroscopic measurements of dark matter halos offer a unique opportunity to determine the underlying properties of dark matter across the vast landscape of dark matter theories. This white paper summarizes the ongoing rapid development of theoretical and experimental methods, as well as new opportunities, to use dark matter halo measurements as a pillar of dark matter physics.

hep-ph↗

arXiv2021

An illustration of canonical quantum-classical dynamics

Using the example of the harmonic oscillator, we illustrate the use of hybrid dynamical brackets in analyzing quantum-classical interaction. We only assume that a hybrid dynamical bracket exists, is bilinear, and reduces to the pure quantum/classical bracket when acting on pure quantum/classical variables. Any hybrid bracket obeying these natural requirements will produce the same dynamics for pure classical or quantum variables, given a hybrid Hamiltonian. Backreaction is manifested in the evolution of a nonvanishing commutator between classical variables. The more massive the classical system is, the less it is affected by backreaction. Interestingly, we show that while pure variables evolve to violate the pure canonical relations, they always obey the hybrid canonical relations. The dynamics of hybrid variables, on the other hand, is shown to require a fully specified and consistent hybrid bracket, otherwise evolution cannot be defined.

quant-ph↗

arXiv2020

Quantum-Classical Dynamical Brackets

We study the problem of constructing a general hybrid quantum-classical bracket from a partial classical limit of a full quantum bracket. Introducing a hybrid composition product, we show that such a bracket is the commutator of that product. From this we see that the hybrid bracket will obey the Jacobi identity and the Leibniz rule provided the composition product is associative. This suggests that the set of hybrid variables belonging to an associative subalgebra with the composition product will have consistent quantum-classical dynamics. This restricts the class of allowed quantum-classical interaction Hamiltonians. Furthermore, we show that pure quantum or classical variables can interact in a consistent framework, unaffected by no-go theorems in the literature or the restrictions for hybrid variables. In the proposed scheme, quantum backreaction appears as quantum-dependent terms in the classical equations of motion.

quant-ph↗

arXiv2019

Probing the origin of our Universe through cosmic microwave background constraints on gravitational waves

The next generation of instruments designed to measure the polarization of the cosmic microwave background (CMB) will provide a historic opportunity to open the gravitational wave window to the primordial Universe. Through high sensitivity searches for primordial gravitational waves, and tighter limits on the energy released in processes like phase transitions, the CMB polarization data of the next decade has the potential to transform our understanding of the laws of physics underlying the formation of the Universe.

astro-ph.CO↗

arXiv2019

Astro2020 Science White Paper: Cosmology with a Space-Based Gravitational Wave Observatory

There are two big questions cosmologists would like to answer -- How does the Universe work, and what are its origin and destiny? A long wavelength gravitational wave detector -- with million km interferometer arms, achievable only from space -- gives a unique opportunity to address both of these questions. A sensitive, mHz frequency observatory could use the inspiral and merger of massive black hole binaries as standard sirens, extending our ability to characterize the expansion history of the Universe from the onset of dark energy-domination out to a redshift z ~ 10. A low-frequency detector, furthermore, offers the best chance for discovery of exotic gravitational wave sources, including a primordial stochastic background, that could reveal clues to the origin of our Universe.

astro-ph.CO↗