Quantum States Of Particles Research Articles

Analyzing the Time Evolution of a Particle by Decomposes the Initial State Confinement in 1D Well into the Lowest Eigenstates Energy

In this work, we obtained the time evolution of the wave function of a limited quantum system (1D Box), hence getting a mathematical model to describe the system. By using programming computes, it performs a time evolution that decomposes the initial state into the 2,10, and 20 lowest energy eigenstates. Finally, by comparing numerical de-composition coefficients for the wave function to the analytical values, it found the number of knots increases directly versus the energy of the particle's quantum state. As a result, the mean bending given by the second derivative which is proportional to the kinetic energy operator should increase. We found there is a negligible mean and standard deviation of the energy in units of the ground state energy.

Information theoretic clustering for coarse-grained modeling of non-equilibrium gas dynamics

We present a new framework towards the objective of learning coarse-grained models based on the maximum entropy principle. We show that existing methods for assigning clusters using the maximum entropy approach are heuristic or sub-optimal. We propose a machine learning framework informed by rate-distortion theory to learn optimal cluster assignments, aiming to improve the effectiveness of the coarse-graining process. Our approach involves transforming the discrete optimization problem into a probabilistic and continuous form. Our inverse modeling approach involves the development of a fully differentiable, adjoint-driven dynamics solver for use with gradient-based optimization techniques. The entire framework is end-to-end differentiable, facilitating backward pass gradient computation to flow through the ODE solve and probabilistic coarse-graining to train a classifier. We demonstrate application in the evolution of particle quantum states in non-equilibrium conditions. The high dimensionality of these equations poses a significant challenge for efficient and accurate computations, even for seemingly simple chemical systems. Training is performed using a loss function informed by rate-distortion theory to cluster the rovibrational states of some molecule, effectively forming a reduced order model of the master equations. We also introduce variable transformations along with several ways of improving the tractability of the training process. These allow the framework to process the extremely high-dimensional discrete optimization problem successfully. Our method is general, and to demonstrate the effectiveness in a controlled setting, we apply it to a one-dimensional Gaussian source quantization problem for which an analytical solution is known, followed by the problem of isothermal relaxation of a ▪ system with O(104) degrees of freedom.

Implementation of Quantum Optimization Algorithm

Quantum computing is a quickly growing research field. This article introduces the basic concepts of quantum computing, recent developments in quantum searching Quantum computers are computing devices that can theoretically have computed power that is many orders of magnitude greater than that of conventional computers. The quantum bit, or qubit, which is the quantum state of electrons in an atom, is the fundamental data unit in a quantum computer. Qubits have the potential to exist in several superposed states at once, making them capable of carrying much more data than do standard two-state bits. The mathematical basis of the proportionality of qubit states is like that of the input weights of neural networks. The technology of quantum computers has made some progress, but much more work needs to be done in terms of research and development before it can be used in everyday life. There are also views that suggest this outcome is impossible. A recent field of study known as quantum computing (QC) combines components of computing, physics, and mathematics. Interest in quantum computing is rising among academics, technologists, and businesspeople. For the past ten years, it has given researchers in the scientific, technological, and industrial disciplines a place to conduct their work. The fundamentals of QC have been developed using notions from quantum physics. The parallel processing functionality in QC has simplified the currently employed algorithms. Numerous optimization-related challenges and issues were solved with the aid of this function. Intelligent computational techniques that were inspired by quantum mechanics have been applied in a variety of fields. A qubit's ability to be in superposition is one of its characteristics that distinguishes it from a conventional bit. Superposition is one of the fundamental principles. Entanglement is another one of quantum physics' counterintuitive occurrences. When each particle's quantum state cannot be characterized separately from the quantum state of the other particle(s), a pair or group of particles are said to be entangled

Quantum trans-Planckian physics inside black holes and its spectrum

We provide a quantum unifying picture for black holes of all masses and their main properties covering classical, semiclassical, Planckian, and trans-Planckian gravity domains: space-time, size, mass, vacuum (``zero-point'') energy, temperature, partition function, density of states, and entropy. Novel results of this paper are that black hole interiors are always quantum, trans-Planckian, and of constant curvature. This is so for all black holes, including the most macroscopic and astrophysical ones. The black hole interior trans-Planckian vacuum is similar to the earliest cosmological vacuum, where the classical gravity dual is the low energy gravity vacuum---today, dark energy. There is no singularity boundary at $r=0$; the quantum space-time is regular. We display the quantum Penrose diagram of the Schwarzschild-Kruskal black hole. The complete black hole instanton (imaginary time) covers the known classical Gibbons-Hawking instanton plus a new, central, highly dense quantum core of Planck length radius and constant curvature. The complete partition function, entropy, temperature, decay rate, discrete levels, and density of states all include the trans-Planckian domain. The semiclassical black hole entropy (the Bekenstein-Hawking entropy) $(\sqrt{n}{)}^{2}$ ``interpolates'' between the quantum point particle entropy ($n$) and the quantum string entropy $\sqrt{n}$, while the quantum trans-Planckian entropy is $1/(\sqrt{n}{)}^{2}$. Black hole evaporation finishes in a pure (nonmixed) quantum state of particles, gravitons, and radiation.

Casting Rubik’s Group into a Unitary Representation for Reinforcement Learning

Rubik’s Cube is one of the most famous combinatorial puzzles involving nearly 4.3 × 1019 possible configurations. However, only a single configuration matches the solved one. Its mathematical description is expressed by the Rubik’s group, whose elements define how its layers rotate. We develop a unitary representation of the Rubik’s group and a quantum formalism to describe the Cube based on its geometrical constraints. Using single particle quantum states, we describe the cubies as bosons for corners and fermions for edges. By introducing a set of four Ising-like Hamiltonians, we managed to set the solved configuration of the Cube as the global ground state for all the Hamiltonians. To reach the ground state of all the Hamiltonian operators, we made use of a Deep Reinforcement Learning algorithm based on a Hamiltonian reward. The Rubik’s Cube is successfully solved through four phases, each phase driven by a corresponding Hamiltonian reward based on its energy spectrum. We call our algorithm QUBE, as it employs quantum mechanics to tackle the combinatorial problem of solving the Rubik’s Cube. Embedding combinatorial problems into the quantum mechanics formalism suggests new possible algorithms and future implementations on quantum hardware.

Inherent color symmetry in quantum Yang-Mills theory

We present the basic non-perturbative structure of the space of classical dynamical solutions and corresponding one particle quantum states in SU(3) Yang-Mills theory. It has been demonstrated that the Weyl group of su(3) algebra plays an important role in constructing non-perturbative solutions and leads to profound changes in the structure of the classical and quantum Yang-Mills theory. We show that the Weyl group as a non-trivial color subgroup of SU(3) admits singlet irreducible representations on a space of classical dynamical solutions which lead to strict concepts of one particle quantum states for gluons and quarks. The Yang-Mills theory is a non-linear theory and, in general, it is not possible to construct a Hilbert space of classical solutions and quantum states as a linear vector space, so, usually, a perturbative approach is applied. We propose a non-perturbative approach based on Weyl symmetric solutions to full non-linear equations of motion and construct a full space of dynamical solutions representing an infinite but countable solution space classified by a finite set of integer numbers. It has been proved that the Weyl singlet structure of classical solutions provides the existence of a stable non-degenerate vacuum which serves as a main precondition of the color confinement phenomenon. Some physical implications in quantum chromodynamics are considered.

Quantisation of the elliptical Penning trap

We present the quantum theory of the elliptical Penning trap, i.e. the general case where the cylindrical symmetry of the electrostatic trapping potential around the trapping magnetic field axis is broken. The theory applies to both slightly and highly elliptical traps, where it is shown that the difference between the quantum states of particles in these traps corresponds to a variation of the degree of squeezing of their motional modes in the xy-plane. In a trap with tunable ellipticity, such as the Geonium Ghip planar Penning trap, it follows that control of the ellipticity via the trapping voltages enables squeezing of the quantum states of the particle. We discuss the adiabatic preparation of such squeezed states, which follows naturally from the appearance of an avoided crossing between the diabatic levels of the coupled motional states of the particle.

A magneto-gravitational trap for studies of gravitational quantum states

Observation time is the key parameter for improving the precision of measurements of gravitational quantum states of particles levitating above a reflecting surface. We propose a new method of long confinement in such states of atoms, anti-atoms, neutrons and other particles possessing a magnetic moment. The earth gravitational field and a reflecting mirror confine particles in the vertical direction. The magnetic field originating from electric current passing through a vertical wire confines particles in the radial direction. Under appropriate conditions, motions along these two directions are decoupled to a high degree. We estimate characteristic parameters of the problem, and list possible systematic effects that limit storage times due to the coupling of the two motions.

Symmetries of free massless particles and soft theorems

In an earlier paper we have constructed a basis of massless single particle quantum states which transform in the unitary principal series representation of the four dimensional Lorentz group. The S-matrix written in this basis gives rise to the Mellin transformed amplitude of Pasterski-Shao-Strominger and its generalization. In this basis the particle can be thought of as living on the null-infinity in the Minkowski space. In this paper we take some preliminary steps to see how the connection between soft theorems and symmetries work out in this picture. For simplicity we consider only the leading soft photon and soft graviton theorems which are related to U(1) Kac-Moody and supertranslations.

Bosonic particle-correlated states: A nonperturbative treatment beyond mean field

Many useful properties of dilute Bose gases at ultra-low temperature are predicted precisely by the (mean-field) product-state Ansatz, in which all particles are in the same quantum state. Yet, in situations where particle-particle correlations become important, the product Ansatz fails. To include correlations nonperturbatively, we consider a new set of states: the particle-correlated state of $N=l\times n$ bosons is derived by symmetrizing the $n$-fold product of an $l$-particle quantum state. The particle-correlated states can be simulated efficiently for large $N$, because their parameter spaces, which depend on $l$, do not grow with $n$. Here we formulate and develop in great detail the pure-state case for $l=2$, where the many-body state is constructed from a two-particle pure state. These paired wave functions, which we call pair-correlated states (PCS), were introduced by A. J. Leggett [Rev. Mod. Phys. ${\bf 73}$, 307 (2001)] as a particle-number-conserving version of the Bogoliubov approximation. We present an iterative algorithm that solves for the reduced (marginal) density matrices (RDMs), i.e., the correlation functions, associated with PCS in time $O(N)$. The RDMs can also be derived from the normalization factor of PCS, which is derived analytically in the large-$N$ limit. To test the efficacy of PCS, we analyze the ground state of the two-site Bose-Hubbard model by minimizing the energy of the PCS~state, both in its exact form and in its large-$N$ approximate form, and comparing with the exact ground state. For $N=1\,000$, the relative errors of the ground-state energy for both cases are within $10^{-5}$ over the entire parameter region from a single condensate to a Mott insulator. We present numerical results that suggest that PCS might be useful for describing the dynamics in the strongly interacting regime.

Согласование теории относительности, ЭПР-эффекта и неравенств Белла через индивидуальное состояние квантовой частицы

Рассматривается эффект Эйнштейна, Подольского, Розена в его связи с квантовой механикой и теорией относительности. Показано, что если ввести в квантовую механику понятие индивидуального состояния квантовой частицы в ансамбле, то можно устранить противоречие с теорией относительности, которое получило название дальнодействия между коррелированными частицами. В работе развит аппарат введения индивидуального состояния в формализм квантовой механики. Строится модель эффекта ЭПР, не содержащая противоречия. Анализируется общий механизм формирования законов теории вероятности в квантовой механике, примером которого является нарушение неравенств Белла для скрытых параметров.

Imaging of Condensed Quantum States in the Quantum Hall Effect Regime

It has been proposed already some time ago that Wigner crystallization in the tails of the Landau levels may play an important role in the quantum Hall regime. Here we use numerical simulations for modelling condensed quantum states and propose real space imaging of such highly correlated electron states by scanning gate microscopy (SGM). The ingredients for our modelling are a many particle model that combines a self-consistent Hartree-Fock calculation for the steady state with a non-equilibrium network model for the electron transport.If there exist condensed many particle quantum states in our electronic model system, our simulations demonstrate that the response pattern of the total sample current as a function of the SGM tip position delivers detailed information about the geometry of the underlying quantum state. For the case of a ring shaped dot potential in the few electron limit it is possible to find regimes with a rigid (condensed) charge distribution in the ring, where the SGM pattern corresponds to the probability density of the quantum states. The existence of the SGM image can be interpreted as the manifestation of an electron solid, since the pattern generation of the charge distribution requires certain stability against the moving tip potential.

Relating quantum discord with the quantum dense coding capacity

We establish the relations between quantum discord and the quantum dense coding capacity in (n + 1)-particle quantum states. A necessary condition for the vanishing discord monogamy score is given. We also find that the loss of quantum dense coding capacity due to decoherence is bounded below by the sum of quantum discord. When these results are restricted to three-particle quantum states, some complementarity relations are obtained.

States of a quantum particle exhibiting complex quasi-energy in a dynamic trap

States of a single quantum particle in a one-dimensional dynamic trap, which correspond to complex values of quasi-energy, are found. The trap is described by a square potential well with periodic smallamplitude oscillations of barrier position. The specific feature of the problem is the fact that the dynamic trap affords simultaneous localization and excitation of the confined particle. The complex nature of the quasienergy is caused by finite probability of particle escape from the trap due to finite depth of the potential well. Within the framework of the second-order perturbation theory with respect to modulation depth, the dependence of the decay rate of the states on modulation frequency is determined, which proves to be nonmonotonic.

Mixed states of quantum particles and the criterion of coherence

The temporal behavior of packet width as a particle passes through a solid film is considered. The effect of memory is demonstrated.

Carrying qubits with particles whose noninformational degrees of freedom are nonfactorable

A directly measurable parameter quantifying effective indistinguishability of particles as a resource for quantum information transfer and processing is proposed. In contrast to commonly used overlap of quantum states of particles, defined only for factorable states, this measure can be generally applied to any joint state of the particles. The relevance of this generalized measure for photons produced in parametric down-conversion has been experimentally verified. The simplest linear-optical quantum-state-transfer protocol, for which this measure directly determines fidelity of the transferred state, was experimentally tested. It has been found that even if some degrees of freedom of two particles are entangled, the particles can still serve as good carriers of qubits.

Condensates and quasiparticles in inflationary cosmology: Mass generation and decay widths

During de Sitter inflation massless particles of minimally coupled scalar fields acquire a mass and a decay width thereby becoming quasiparticles. For bare massless particles nonperturbative infrared radiative corrections lead to a self-consistent generation of mass, for a quartic self-interaction $M\ensuremath{\propto}{\ensuremath{\lambda}}^{1/4}H$, and for a cubic self-interaction the mass is induced by the formation of a nonperturbative condensate leading to $M\ensuremath{\propto}{\ensuremath{\lambda}}^{1/3}{H}^{2/3}$. These radiatively generated masses restore de Sitter invariance and result in anomalous scaling dimensions of superhorizon fluctuations. We introduce a generalization of the nonperturbative Wigner-Weisskopf method to obtain the time evolution of quantum states that include the self-consistent generation of mass and regulate the infrared behavior. The infrared divergences are manifest as poles in $\ensuremath{\Delta}={M}^{2}/3{H}^{2}$ in the single particle self-energies, leading to a rearrangement of the perturbative series nonanalytic in the couplings. A set of simple rules that yield the leading order infrared contributions to the decay width are obtained and implemented. The lack of kinematic thresholds entail that all particle states acquire a decay width, dominated by the emission and absorption of superhorizon quanta $\ensuremath{\propto}(\ensuremath{\lambda}/H{)}^{4/3}[H/{k}_{ph}(\ensuremath{\eta}){]}^{6}$; $\ensuremath{\lambda}[H/{k}_{ph}(\ensuremath{\eta}){]}^{6}$ for cubic and quartic couplings respectively to leading order in $M/H$. The decay of single particle quantum states hastens as their wave vectors cross the Hubble radius and their width is related to the highly squeezed limit of the bi- or trispectrum of scalar fluctuations respectively.

Semigroups of tomographic probabilities and quantum correlations

Semigroups of stochastic and bistochastic matrices constructed by means of spin tomograms or tomographic probabilities and their relations to the problem of Bell's inequalities and entanglement are reviewed. The probability determining the quantum state of spins and the probability densities determining the quantum states of particles with continuous variables are considered. Entropies for semigroups of stochastic and bisctochastic matrices are studied, in view of both the Shannon information entropy and its generalization like Rényi entropy. Qubit portraits of qudit states are discussed in the connection with the problem of Bell's inequality violation for entangled states.

Knotted Picture of Unitary Transformation Applied to Single Particle Quantum State

This paper introduces the unified expression of four Bell bases and uses the composition operation in knot theory to obtain the knotted picture of unitary operators based on Pauli operators, and gives the knotted expressions of 12 inversion relations between the four Bell bases.

Instantons and conformal holography

We study a subsector of the AdS_4/CFT_3 correspondence where a class of solutions in the bulk and on the boundary can be explicitly compared. The bulk gravitational theory contains a conformally coupled scalar field with a Phi^4 potential, and is holographically related to a massless scalar with a Phi^6 interaction in three dimensions. We consider the scalar sector of the bulk theory and match bulk and boundary classical solutions of the equations of motion. Of particular interest is the matching of the bulk and the boundary instanton solutions which underlies the relationship between bulk and boundary vacua with broken conformal invariance. Using a form of radial quantization we show that quantum states in the bulk correspond to multiply-occupied single particle quantum states in the boundary theory. This allows us to explicitly identify the boundary composite operator which is dual to the bulk scalar, at the free theory level as well as in the instanton vacuum. We conclude with a discussion of possible implications of our results.