Square-well Research Articles

Lattice QCD and Three-Particle Decays of Resonances

Most strong-interaction resonances have decay channels involving three or more particles, including many of the recently discovered X, Y, and Z resonances. In order to study such resonances from first principles using lattice QCD, one must understand finite-volume effects for three particles in the cubic box used in calculations. We review efforts to develop a three-particle quantization condition that relates finite-volume energies to infinite-volume scattering amplitudes. We describe in detail the three approaches that have been followed, and present new results on the relationship between the corresponding results. We show examples of the numerical implementation of all three approaches and point out the important issues that remain to be resolved.

Hole States in Spherical Quantum Nanoheterosystem with Intermediate Spin-Orbital Interaction

The hole energy spectrum has been studied for the spherical semiconductor nanoheterosystem with the cubic symmetry. The exact solutions of the Schrödinger equation for the ground and excited hole states are presented within the framework of the 6-band Luttinger Hamiltonian and the finite gap of bands with the corresponding boundary conditions. Dependence of the holes energies from the radius of the quantum dot has been calculated for the GaAs/AlAs heterostructure. Obtained results where compared with data obtained using the infinite potential well model, as well as the single-band model for heavy and light holes.

One-dimensional Coulomb system in a sticky wall confinement: Exact results.

This work investigates a one-component one-dimensional Coulomb system in sticky wall confinement. Sticky wall is introduced as an alternative and intuitive depiction of charge regulation, the notion that a surface charge is not a fixed but a fluctuating quantity in dynamic equilibrium with its immediate environment. Emphasis is placed on intuitive derivation and expressions are obtained by observing that the partition function of a charge regulated system can be decomposed into a collection of independent equilibriums with different fixed surface charges. Adsorbed particles behave as ideal-gas particles in a one-dimensional box whose length corresponds to the parameter of stickiness. Among various scenarios considered are a single- and two-wall confinement as well as the case of sticky counterions capable of associating into pairs. Exact solutions provide a view of the role and behavior of surface charge fluctuations, which is an important step in the "beyond-mean-field" analysis. Consequently, the model serves as a simple paradigm of the mechanism that gives rise to the Kirkwood-Shumaker interactions detected in real systems.

Controlling a quantum system via its boundary conditions

We numerically study a particle in a box with moving walls. In the case where the walls are oscillating sinusoidally with a small amplitude, we show that states up to the fourth state can be populated with more than 80 percent population, while higher lying states can also be selectively excited. This work introduces a way of controlling quantum systems which does not rely on (dipole) selection rules.Graphical abstract

Controlled trapping of single particle states on a periodic substrate by deterministic stubbing

Abstract A periodic array of atomic sites, described within a tight binding formalism is shown to be capable of trapping electronic states as it grows in size and gets stubbed by an ‘atom’ or an ‘atomic’ clusters from a side in a deterministic way. We prescribe a method based on a real space renormalization group method, that unravels a subtle correlation between the positions of the side coupled atoms and the energy eigenvalues for which the incoming particle finally gets trapped. We discuss how, in such conditions, the periodic backbone gets transformed into an array of infinite quantum wells in the thermodynamic limit. We present a case here, where the wells have a hierarchically distribution of widths, hosting standing wave solutions in the thermodynamic limit.

Where are the particles when the box is hot?

We consider the known problem of a particle in a one-dimensional box, i.e. in an infinite potential well. Specifically, we evaluate the probability density for finding a particle in a certain position when the system is in contact with a reservoir at a temperature T ≠ 0. We observe that, when the T is increased, the density tends to become uniform in the box, except in a ‘boundary layer’ close to the walls. Then, we consider two particles in the box, discriminating between bosons and fermions. The particles are first analyzed without accounting for the spin. Evaluating the thermalized probability density in this way, results in a clear difference between bosons and spinless fermions. Next, we consider the complete wave function for spin-½fermions, and the probability density changes significantly with respect to the spinless case. This shows that disregarding the electron spin for the sake of simplicity may lead to misleading results.

FLUIDIZATION OF A BED OF SOLID PARTICLES IN A TWO DIMENSIONAL VERTICAL BOX

Simulation of fluidization of a bed of solid particles in a two-dimensional box is performed using molecular dynamics methods by assuming that superposition of buoyant, gravitational, viscous, collision force will make the particle to move in two dimensions. Two different fluid type is used in this simulation, i.e., gas and liquid fluid. By increasing the fluid velocity from small to high, then minimum fluidization condition reached. As a result, fluidization of alumina particle with liquid fluid has a minimum fluidization velocity lower than gas fluid.

Monte Carlo simulation of an associating fluid model to describe polymerization in polycaprolactone diols: The role of attractive sites of variable range

In this work we study the clustering of hard spheres (HS) with associating square-well (SW) sites of variable range as a model of polymerization process, like the ring-opening polymerization of the ϵ-caprolactone. We present a systematic Monte Carlo (MC) computer simulation study of the effects of the interaction parameters on the cluster morphology, characterized by the fractal dimension, and compared with experimental results for the poly(ϵ-caprolactone). The cluster morphology depends on the length and energy scales of the system and both can be related to the intrinsic properties of propagating species.

Square-well self-diffusion coefficients in liquid binary alloys of alkali metals within the mean spherical approximation

The concentration dependencies of the self-diffusion coefficients in liquid Na–K and K–Cs alloys at T = 373 K are calculated in the framework of the linear trajectory approximation in conjunction with the square-well (SW) model treated by the mean spherical approximation in the semi-analytical representation. It is shown that this approach allows to achieve a good description of diffusion properties for liquid binary metal alloys at the same values of the SW parameters that lead to a good description of the structure and entropy for alloys under consideration.

Stochastic thermodynamics of nonharmonic oscillators in high vacuum.

We perform an analytic study on the stochastic thermodynamics of a small classical particle trapped in a time-dependent single-well potential in the highly underdamped limit. It is shown that the nonequilibrium probability density function for the system's energy is a Maxwell-Boltzmann distribution (as in equilibrium) with a closed form time-dependent effective temperature and fractional degrees of freedom. We also find that the solvable model satisfies the Crooks fluctuation theorem, as expected. Moreover, we compute the average work in this isothermal process and characterize analytically the optimal protocol for minimum work. The optimal protocol presents an initial and a final jump which correspond to adiabatic processes linked by a smooth exponential time-dependent part for all kinds of single-well potentials. Furthermore, we argue that this result connects two distinct relevant experimental setups for trapped nanoparticles, the levitated particle in a harmonic trap, and the free particle in a box, as they are limiting cases of the general single-well potential and display the time-dependent optimal protocols. Finally, we highlight the connection between our system and an equivalent model of a gas of Brownian particles.

Optimal strategies to infer the width of an infinite square well by performing measurements on the particle(s) contained in the well

We seek the optimal strategy to infer the width a of an infinite potential well by performing measurements on the particle(s) contained in the well. In particular, we address quantum estimation theory as the proper framework to formulate the problem and to determine the optimal quantum measurement, as well as to evaluate the ultimate bounds to precision. Our results show that in a static framework the best strategy is to measure position on a delocalized particle, corresponding to a width-independent quantum signal-to-noise ratio (QSNR), which increases with delocalisation. Upon considering time-evolution inside the well, we find that QSNR increases with time as t2 (at least for small t). On the other hand, it decreases with a and thus time-evolution is a metrological resource only when the width is not too large compared to the available time evolution. Finally, we consider entangled particles in the well and observe super-additivity of the QSNR: it is the sum of the single-particle QSNRs, plus a positive definite term, which depends on their preparation and may increase with the number of entangled particles. Overall, entanglement represents a resource for the precise characterization of potential wells.

Berry phase for a particle in an infinite spherical potential well with moving wall

Berry phase for a particle in an infinite spherical potential well with moving wall

Bhatia–Thornton fluctuations, transport and ordering in partially ordered Al–Cu alloys

The Bhatia–Thornton (BT) correlation functions namely the number–number, concentration–concentration and number-concentration correlation functions in liquid binary melts are important parameters for understanding the complexities in binary liquids. In this paper, the microscopic BT correlation functions of liquid Al–Cu alloys are investigated using square well (SW) potential under mean spherical model approximation. These correlation functions are linearly related to the Ashcroft–Langreth type partial structure factors. Thermodynamically important microscopic function i.e. concentration–concentration correlation function in the long-wavelength limit, SCC(0) is analytically calculated, which is well-known in BT formalism and is often used to characterized the mixing behavior in binary melts. The Warren–Cowley chemical short range order parameters, as function of Cu concentration is also computed in the liquid Al–Cu alloys through structural studies in the long wavelength limit, which gives valuable information regarding ordering in melts. The compound forming behavior in Al–Cu alloys is evidenced by the results obtained for the value of SCC(0) and . Further, transport properties in binary mixture have been determined by using BT-correlation functions and its long wavelength limit values. Kinetic as well as thermodynamic factors were taken care in the computation of dynamic properties of alloys.

Testing the Detection Significance on the Large-scale Structure by a JWST Deep Field Survey

Abstract In preparation for deep extragalactic imaging with the James Webb Space Telescope, we explore the clustering of massive halos at z = 8 and 10 using a large N-body simulation. We find that halos with masses of 109–1011 h −1 M ⊙, which are those expected to host galaxies detectable with JWST, are highly clustered with bias factors ranging from 5 to 30 depending strongly on mass, as well as on redshift and scale. This results in correlation lengths of 5–10 h −1 Mpc, similar to those of today’s galaxies. Our results are based on a simulation of 130 billion particles in a box of size 250 h −1 Mpc using our new high-accuracy Abacus simulation code, the corrections to cosmological initial conditions of Garrison et al., and the Planck 2015 cosmology. We use variations between sub-volumes to estimate the detectability of the clustering. Because of the very strong interhalo clustering, we find that a medium-sized survey with a transverse size of the order of 25 h −1 comoving Mpc (about 13′) may be able to detect the clustering of z = 8–10 galaxies with only 500–1000 survey objects if the galaxies indeed occupy the most massive dark matter halos.

Quantum to classical transition in an information ratchet.

Recent years have seen a flurry of research activity in the study of minimal and autonomous information ratchets. However, the existing classical and quantum models are somewhat hard to compare and hence quantifying possible quantum supremacy in information ratchets has been elusive. We propose a step towards filling this void between quantum and classical ratchets by introducing a model with continuous variables: a quantum particle in a box coupled to a stream of qubits. The dynamics is solved exactly and we analyze the quantum to classical transition in terms of a natural timescale parameter for the model.

Information-thermodynamics link revisited

The so-called information-thermodynamics link created by a thought experiment of Szilard became a core of modern orthodoxy in the field of quantum information and resources theory in quantum thermodynamics. We recall existing objections against standard interpretation of Szilard engine operation and illustrate them by two quantum models: a particle in a box with time-dependent thin potential barrier and the spin-boson model. The consequences of the emerging superselection rules for thermodynamics and foundations of quantum mechanics are discussed. The role of non-ergodic systems as information carriers and the thermodynamic cost of stability and accuracy of information processing is briefly discussed and compared to the generally accepted Landauer’s principle.

Particles in a Box with One Sticky Wall: From ODE to PDE

We present noncompetitive adsorption as “particles in a box with one sticky wall.” We start with a general model that can be modeled as a simple ordinary differential equation (ODE). To verify the ODE students run a computer simulation. The ODE’s solution imperfectly fits the simulation’s data. This leads to the diffusion partial differential equation. We show how to determine the diffusion constant from theory; how to determine how many terms in the Fourier series solution need to be summed; and the use of nonlinear regression. As a bonus, the physics of the model will lead us to a series representation of π.

Resonant tunneling through a linear potential barrier

Resonant tunneling is a quantum phenomenon that has been extensively studied and applied in electronic devices. In this paper, the transmission coefficient and resonant energies of a particle passing through a linear potential barrier are derived and investigated. We propose that approximated values of resonant energies can be achieved by considering the energy levels of a particle confined in an infinite tilted potential well. It is found that approximation of high resonant energies is more accurate than that of low resonant energies.

Determination of energy levels, probabilities, and expectation values of particles in the three-dimensional box at quantum numbers ≤5

Static potential boxes represent an area that is limited by an infinite potential wall, where there is no external potential in it. The solution of the Schrodinger equation gives a wave function that can explain the energy level and determine the probability of finding a particle at any point. The main focus of the research in this paperwas to solve the solution to the energy levels, probabilities, and expectation values of a particle in a three-dimensional box, where control limits are given for the potential box width, namely and L for each situation. In this research, the results showed that probability meetings depend on changes in box width and quantum number of particles, while particle energy levels depend on the length of the box and the quantum number of particles. Based on the relation between probabilities and expectation values, the most stable size of the box to find the particles in ground state to the fourth excitation state is at the width of and L.

Simulation on debris particles conveying process in lubricant between gear engagement

While the gear engagement working, debris particles are generated and theoretically brought away by flowing lubricant oil. The conveying process of particles in lubricant is helpful to clean up the friction pair, but how are the particles brought out and how does the particles convey in oil are still unknown. Electrostatic sensor can be used to monitor the debris particles in lubricant while the friction pairs are working. If the debris distribution in lubricant can be known before the installation of the sensor, it may get a chance to position the sensor on the way where particle concentration is the highest. The research result can be used to guide the installation of electrostatic sensor and increase the output efficiency of the sensor. In this paper, the CFD method is used to study the conveying process of particles, combined with the Dynamic Mesh technology and the DPM model, and an external gear box is taken as an example for analysis. Different sizes of particles are put into the lubricant oil flow field, and the trajectories and distribution of particles are calculated by simulation. The calculated result found that: The movement of the particles in the gear box is very complicated, with a large randomness. All the particles show a tendency of centrifugal movement, most of the particles are distributed close to the inner wall of the box and less far away from inner wall of the box. When the particles are flushed out from the gear box, they are more distributed in the lower half of the pipe. The small particles have a better followability in oil flow and are easy to be affected by turbulence. And when they are discharged from gear box into the pipeline, the average velocity of them are larger. Whereas the large particles are in contrary. In addition, the faster the gear's working speed and the smaller the centre distance (engagement gap) are, the more significant the particle is affected by turbulence, and the particle trajectory shows greater cross-disorder and randomness. The average velocity of particles motion has a nonlinear positive and negative relationship with gear speed and centre distance.