Harmonic Potential Research Articles

Particle number and interactions in the entropic uncertainty relations

The dependence of the entropic uncertainty relations on particle number and on attractive and repulsive interparticle potential strengths, is examined in the ground state of coupled harmonic oscillators. The reduced entropy sums depend on the normalization constants of the position and momentum densities, which in turn depend on particle number and interaction strength. These sums exhibit maxima as the particle number is varied, when the particles are in the presence of attractive potentials. On the other hand, no maxima are observed for systems with a repulsive potential. All reduced entropy sums increase and move away from the bound with greater interactions. Consistent behaviours are observed for both reduced one- and two-variable entropy sums. Further reductions of the N-particle densities induce that the respective entropy sums are now farther away from the corresponding bounds. The interpretation of these results is that reduction and increased interaction translates into a weakening of the strength of the uncertainty principle statement. The one- and two-variable entropy sums of these systems are shown to approximate the relation, when the intensity of the one-body harmonic potential is set at the number of particles.

Quantum Otto-type heat engine with fixed frequency.

In this work we analyze an Otto-type cycle operating with a working substance composed of a quantum harmonic oscillator (QHO). Unlike other studies in which the work extraction is done by varying the frequency of the QHO and letting it thermalize with a squeezed reservoir, here we submit the QHO to a parametric pumping controlled by the squeezing parameter and let it thermalize with a thermal reservoir. We then investigate the role of the squeezing parameter in our Otto-type engine powered by parametric pumping and show that it is possible to reach the Carnot limit by arbitrarily increasing the squeezing parameter. Notably, for certain squeezing parameters r, e.g., r=0.4, the quasistatic Otto limit can be reached even at nonzero power. We also investigated the role of entropy production in the efficiency behavior during the unitary strokes, showing that positive (negative) changes in entropy production correspond to increases (decreases) in engine efficiency, as expected. Furthermore, we show that under thermal reservoirs a work extraction process that is more efficient than the Carnot engine is impossible, regardless of the quantum resource introduced via the Hamiltonian of the system.

Zombie cats on the quantum-classical frontier: Wigner-Moyal and semiclassical limit dynamics of quantum coherence in molecules.

In this paper, we investigate the time evolution of quantum coherence-the off-diagonal elements of the density matrix of a multistate quantum system-from the perspective of the Wigner-Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit-an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable.

Superfluidity nature of interacting rotating ultracold boson atoms trapped in an optical potential that overlaps with a harmonic potential

This paper explores the superfluidity nature of the rotating ultracold boson atoms trapped in an overlapping optical potential with harmonic potential in three dimensions at finite temperature. The number of vortices, the critical rate of rotation for the formation of vortices, and the superfluid fraction have all been determined. These parameters required to calculate thermal average of the in situ size and the angular momentum expectation values. Calculations of the mentioned parameters are made using the proper semiclassical approximation. For upcoming BEC experiments in these traps, the outcome results provide useful qualitative theoretical insights. Additionally, they give the current experiment by Greiner et al. (2002) a strong theoretical basis.

Asymmetric solitons induced by transition and beating effects

We investigate the dynamics of beating solitons in a two-component Bose–Einstein condensate with tunable Rabi coupling strength. Our results demonstrate that the balance between transition and beating effects permits the emergence of a novel family of asymmetric solitons in the symmetric physical settings. We derive the exact analytical solutions for them, which primarily consist of one bright soliton and one dark soliton element. The analytical solutions provide us with precise balance conditions required for the formation of asymmetric solitons. We also show that the degree of asymmetry can be effectively manipulated by adjusting the background density flow of dark soliton element, initial relative phase between two soliton elements, and their width. Furthermore, we discuss the oscillation behavior of asymmetric solitons in a harmonic potential, and the interaction between them.

ExoMol line lists – LVI. The SO line list, MARVEL analysis of experimental transition data and refinement of the spectroscopic model

ABSTRACT A semi-empirical IR/Vis line list, SOLIS, for the sulphur monoxide molecule 32S16O is presented. SOLIS includes accurate empirical rovibrational energy levels, uncertainties, lifetimes, quantum number assignments, and transition probabilities in the form of Einstein A coefficients covering the $X\, {}^{3}\Sigma ^{-}$$, a\, {}^{1}\Delta , b\, {}^{1}\Sigma ^{+}, A\, {}^{3}\Pi , B\, {}^{3}\Sigma ^{-}, A^{\prime \prime }\, {}^{3}\Sigma ^{+}, A^{\prime }\, {}^{3}\Delta$, and $e\, {}^{1}\Pi$ systems and wavenumber range up to 43 303.5 cm−1 (≥230.93 nm) with J ≤ 69. SOLIS has been computed by solving the rovibronic Schrödinger equation for diatomics using the general purpose variational code Duo and starting from a published ab initio spectroscopic model of SO (including potential energy curves, coupling curves, (transition) dipole moment curves) which is refined to experimental data. To this end, a database of 50 106 experimental transitions, 48 972 being non-redundant, has been compiled through the analysis of 29 experimental sources, and a self-consistent network of 8558 rovibronic energy levels for the X, a, b, A, B, and C electronic states has been generated with the marvel algorithm covering rotational and vibrational quantum numbers J ≤ 69 and v ≤ 30 and energies up to 52 350.40 cm−1. No observed transitions connect to the $B\, {}^{3}\Sigma ^{-}$(v = 0) state which is required to model perturbations correctly, so we leave fitting the $B\, {}^3\Sigma ^-$ and $C\, {}^3\Pi$ state UV model to a future project. The SO line list is available at ExoMol from www.exomol.com.

Entanglement and Symmetry Structure of N(= 3) Quantum Oscillators with Disparate Coupling Strengths in a Common Quantum Field Bath

In this paper, we study the entanglement structure of a system of N quantum oscillators with distinctive coupling strengths, all linearly coupled to a common massless scalar quantum field. This study is helpful in characterizing the notion of an entanglement domain and its symmetry features, which is useful for understanding the interplay between different levels of structure in many-body quantum systems. The effect of the quantum field on the system is derived via the influence functional and the correlation functions are obtained from the solutions of the evolutionary operator of the reduced density matrix. They are then used to construct the covariance matrix, which forms the basis for our analysis of the structure of quantum entanglement in this open system. To make the physical features explicit, we consider a system of three quantum coupled oscillators placed at the vertices of an equilateral triangle with disparate pairwise couplings. We analyze the entanglement between one oscillator and the other two with equal (symmetric) and unequal (asymmetric) coupling strengths. As a physical illustration, we apply the results for these two different configurations to address some basic issues in macroscopic quantum phenomena from the quantum entanglement perspective.

Rotating quantum droplets confined in a harmonic potential

Rotating quantum droplets confined in a harmonic potential

High-Precision Calculation of Nanoparticle (Nanocrystal) Potentials of Mean Force and Internal Energies.

Thermodynamic stability assessment of nanocrystal systems requires precise free energy calculations. This study highlights the importance of meticulous control over various factors, including the thermostat, time step, potential cutoff, initial configuration, sampling method, and overall simulation duration. Free energy computations in dry (solvent-free) systems are on the order of several hundred kBT but can be obtained with consistent accuracy. However, calculation of internal energies becomes challenging, as they are typically much larger in magnitude than free energies and exhibit significant noise and reduced reliability. To address this limitation, we propose a new internal energy estimate that drastically reduces the noise. We also present formulas that enable the optimization of the parameters of the harmonic bias potential for optimal convergence. Finally, we discuss the implications of these findings for the computation of free energies in nanocrystal clusters and superlattices.

First-passage time statistics for non-linear diffusion

Most processes examined from a standpoint of the first-passage problem are modeled by linear diffusion equations. Here, we consider the non-linear diffusion equation in which diffusivity is power-law dependent on the concentration/probability density and explore its fundamental first-passage properties. Depending on the value of the power-law exponent, we demonstrate the exact and approximate expressions for the survival probability and the first-passage time distribution along with their asymptotic representations. These results refer to the freely and harmonically trapped diffusing particle. While in the former case the mean first-passage time is divergent, albeit the first-passage time distribution is normalized to unity, it is finite in the latter. To support this result, we derive the exact formula for the mean first-passage time to the target prescribed in the minimum of the harmonic potential.

Empirical rovibrational energy levels for carbonyl sulphide

ABSTRACT An exhaustive review of the measured rovibrational transitions of the 16 O 12 C 32 S isotopologue of carbonyl sulphide is undertaken. A comprehensive analysis of data from 100 papers is carried out using a consistent set of harmonic oscillator quantum numbers which are recommended for future studies. A corrected compilation of 14,071 OCS transitions is then subjected to a Measured Active Rotational-Vibrational Energy Levels (MARVEL) analysis, resulting in 5729 empirical energy levels. The uncertainties corresponding to these levels are analysed using different procedures; the newly implemented bootstrap method is used to provide final uncertainties.

Is a loopy and noncommutative early Universe viable?

We conduct a (pre-)inflationary dynamics study of the chaotic quadratic potential within the framework of a simple noncommutative extension of effective loop quantum cosmology put forward recently. It is concluded that, for typically small values of the noncommutativity parameter, the resulting (pre-)inflationary scenario is essentially indistinguishable from the one corresponding to standard loop quantum cosmology.

Quantum uncertainty as an intrinsic clock

In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom. For instance, in the semi-classical regime, while the position and momentum expectation values follow the classical trajectory, the uncertainty of a wave-packet can evolve and beat independently. We use this insight to revisit the dynamics of a 1d particle in a time-dependent harmonic well. One can solve it by considering time reparameterizations and the Virasoro group action to map the system to the harmonic oscillator with constant frequency. We prove that identifying such a simplifying time variable is naturally solved by quantizing the system and looking at the evolution of the width of a Gaussian wave-packet. We further show that the Ermakov-Lewis invariant for the classical evolution in a time-dependent harmonic potential is actually the quantum uncertainty of a Gaussian wave-packet. This naturally extends the classical Ermakov-Lewis invariant to a constant of motion for quantum systems following Schrödinger equation. We conclude with a discussion of potential applications to quantum gravity and quantum cosmology.

Just some simple (but nontrivial) analytical solutions for de Broglie–Bohm quantum cosmology

In this work, we provide some simple analytical solutions to the Wheeler–DeWitt equation for the minisuperspace applied to de Broglie–Bohm quantum cosmology for particular potentials of a scalar matter field ϕ. One solution describes a constantly rolling scalar field with a quadratic potential plus a negative cosmological constant. The scale factor is given by a Gaussian function. The other solution describes a flat Minkowski universe with the potential of a hilltop form.

Powering quantum Otto engines only with q-deformation of the working substance.

We consider a quantum Otto cycle with a q-deformed quantum oscillator working substance and classical thermal baths. We investigate the influence of the quantum statistical deformation parameter q on the work and efficiency of the cycle. In usual quantum Otto cycle, a Hamiltonian parameter is varied during the quantum adiabatic stages while the quantum statistical character of the working substance remains fixed. We point out that even if the Hamiltonian parameters are not changing, work can be harvested by quantum statistical changes of the working substance. Work extraction from thermal resources using quantum statistical mutations of the working substance makes a quantum Otto cycle without any classical analog.

Accurate Thermodynamic Properties of Ideal Bosons in a Highly Anisotropic 2D Harmonic Potential.

One can derive an analytic result for the issue of Bose-Einstein condensation (BEC) in anisotropic 2D harmonic traps. We find that the number of uncondensed bosons is represented by an analytic function, which includes a series expansion of q-digamma functions in mathematics. One can utilize this analytic result to evaluate various thermodynamic functions of ideal bosons in 2D anisotropic harmonic traps. The first major discovery is that the internal energy of a finite number of ideal bosons is a monotonically increasing function of anisotropy parameter p. The second major discovery is that, when p≥0.5, the changing with temperature of the heat capacity of a finite number of ideal bosons possesses the maximum value, which happens at critical temperature Tc. The third major discovery is that, when 0.1≤p<0.5, the changing with temperature of the heat capacity of a finite number of ideal bosons possesses an inflection point, but when p<0.1, the inflection point disappears. The fourth major discovery is that, in the thermodynamic limit, at Tc and when p≥0.5, the heat capacity at constant number reveals a cusp singularity, which resembles the λ-transition of liquid helium-4. The fifth major discovery is that, in comparison to 2D isotropic harmonic traps (p=1), the singular peak of the specific heat becomes very gentle when p is lowered.

Visualizations and Analyses of Quantum Behavior, Spacetime Curvature, and Metric Relationships in Relativistic Physics

This study aims to investigate essential concepts in quantum mechanics and theoretical physics, with an emphasis on the 1+1 dimension. We examine the Dirac equation for relativistic spin-1/2 particles, the Time-Dependent Schrödinger Equation in 1+1 spacetime with flat conformal metric, and connect them to the Dirac equation. Additionally, we explore the Alcubierre Metric related to warp drive, particle modeling in a harmonic potential using the Schrödinger Equation, and the Gödel Metric Solution to depict the peculiarities of spacetime. The research aims to deepen the understanding of these concepts, identify theoretical implications, and their potential applications. This research aims to enhance the understanding of fundamental physics, assist in the development of future technologies, and provide deeper insights into the universe. Its benefits lie in contributing to theoretical understanding in physics, which can spark the development of new theories. This study is limited to physics concepts in the 1+1 dimensions, without empirical experiments or practical applications. The primary focus is on the theoretical analysis of these concepts. The results of this research have potential theoretical implications in understanding basic physics and spacetime phenomena. The simplification and connections between these concepts can aid in the development of new theories in theoretical physics. The uniqueness of this research lies in its integrative approach to quantum mechanics and theoretical physics concepts in the 1+1 dimension, which may not have been extensively explored previously. Through this research, we have investigated several key concepts in quantum mechanics and theoretical physics in the 1+1 dimension. These findings can make a significant contribution to our understanding of the universe and the potential development of new theories in physics.

Primordial black holes from a curvaton scenario with strongly non-Gaussian perturbations

We investigate the production of primordial black holes (PBHs) in a mixed inflaton-curvaton scenario with a quadratic curvaton potential, assuming the curvaton is in de Sitter equilibrium during inflation with 〈χ〉 = 0. In this setup, the curvature perturbation sourced by the curvaton is strongly non-Gaussian, containing no leading Gaussian term. We show that for m 2/H 2 ≳ 0.3, the curvaton contribution to the spectrum of primordial perturbations on CMB scales can be kept negligible but on small scales the curvaton can source PBHs. In particular, PBHs in the asteroid mass range 10-16 M ⊙ ≲ M ≲ 10-10 M ⊙ with an abundance reaching F PBH = 1 can be produced when the inflationary Hubble scale H ≳ 1012 GeV and the curvaton decay occurs in the window from slightly before the electroweak transition to around the QCD transition.

Order, Chaos and Born’s Distribution of Bohmian Particles

We study order, chaos and ergodicity in the Bohmian trajectories of a 2D quantum harmonic oscillator. We first present all the possible types (chaotic, ordered) of Bohmian trajectories in wavefunctions made of superpositions of two and three energy eigenstates of the oscillator. There is no chaos in the case of two terms and in some cases of three terms. Then, we show the different geometries of nodal points in bipartite Bohmian systems of entangled qubits. Finally, we study multinodal wavefunctions and find that a large number of nodal points does not always imply the dominance of chaos. We show that, in some cases, the Born distribution is dominated by ordered trajectories, something that has a significant impact on the accessibility of Born’s rule P=|Ψ|2 by initial distributions of Bohmian particles with P0≠|Ψ0|2.

A quantum Otto engine with shortcuts to thermalization and adiabaticity

We investigate the energetic advantage of accelerating a quantum harmonic oscillator Otto engine by use of shortcuts to adiabaticity (for the expansion and compression strokes) and to equilibrium (for the hot isochore), by means of counter-diabatic (CD) driving. By comparing various protocols with and without CD driving, we find that, applying both type of shortcuts leads to enhanced power and efficiency even after the driving costs are taken into account. The hybrid protocol not only retains its advantage in the limit cycle, but also recovers engine functionality (i.e. a positive power output) in parameter regimes where an uncontrolled, finite-time Otto cycle fails. We show that controlling three strokes of the cycle leads to an overall improvement of the performance metrics compared with controlling only the two adiabatic strokes. Moreover, we numerically calculate the limit cycle behavior of the engine and show that the engines with accelerated isochoric and adiabatic strokes display a superior power output in this mode of operation.