Klein-Gordon Equation and Wave Function for Free Particle in Rindler Space-Time

Klein-Gordon equation is a relativistic wave equation. It treats spinless particle. The wave functioncannot use as a probability amplitude. We made Klein-Gordon equation in Rindler space-time. In this paper,we make free particle’s wave function as the solution of Klein-Gordon equation in Rindler space-time.

The radiation of a spin-free particle in the field of a plane electromagnetic wave

In this paper, we obtained a solution for the equation of motion of a charged spinless particle in the field of a plane electromagnetic wave. Relativistic expressions for the cross section of Compton scattering by a charged particle of spin 0 interacting with the field of a plane electromagnetic wave are calculated. Numerical simulation of the total probability of radiation as the function of the electromagnetic wave amplitude is carried out. The radiation probability is found to be consistent with the total cross section for Compton scattering by a charged particle of spin 0.

Energy exchange calculations in a simple mechanical system to investigate the origin of friction

The microscopic origin of friction is an important topic in science and technology. To date, noteworthy aspects of it remain unsolved. In an effort to shed some light on the possible mechanisms that could give rise to the macroscopic emergence of friction, a very simple 1D system of two particles is considered, one of them is free but moving with an initial velocity, and the other confined by a harmonic potential. The two particles interact via a repulsive Gaussian potential. While it represents in a straightforward manner a tip substrate system in the real world, no analytic solutions can be found for its motion. Because of the interaction, the free particle (tip) may overcome the bound particle (substrate) losing part of its kinetic energy. We solve Newton’s equations of the two particles numerically and calculate the net exchange of energy in the asymptotic state in terms of the relevant parameters of the problem. The effective dissipation that emerges from this simple, classical model with no ad hoc terms shows, surprisingly, a range of rich, nontrivial, behavior. We give theoretical reasoning which provides a satisfactory qualitative description. The essential ingredient of that reasoning is that the transfer of energy from the incoming particle to the confined one can be regarded as the source of the emergent dissipation force the friction experienced by the incoming particle.

Quaternionic Dirac free particle

In this paper, we solve the quaternionic Dirac equation [Formula: see text] in the real Hilbert space, and we ascertain that their free particle solutions set comprises eight elements in the case of a massive particle, and a four elements solutions set in the case of a massless particle, a richer situation when compared to the four elements solutions set of the usual complex Dirac equation [Formula: see text]. These free particle solutions were unknown in the previous solutions of anti-Hermitian quaternionic quantum mechanics, and constitute an essential element in order to build a quaternionic quantum field theory [Formula: see text].

ON THE STRUCTURE OF THE CONFIGURATION SPACE OF CHARGED BLACK HOLES

Some properties of the configuration space (CS) of charged black holes (BH) we are considered. A reduced action for the spherically symmetric configuration of the gravitational and electromagnetic fields is constructed. We restrict ourselves to considering of T-region, where the studied fields have a dynamic meaning. Using the Hamiltonian constraint, we exclude the nondynamic degree of freedom. This leads to the action of the system in the CS with the corresponding supermetric. It turns out that the CS is flat, and its metric admits a twoparametric group of motions. This group generates conservation laws for the geodesic equations. The first law is the charge conservation law, and second is the mass conservation law (the mass function). Using the Hamiltonian constraint, they allow one to find momenta as a function of the field variables andcalculate the action as a function of the conserved quantities and field variables in CS. We emphasize that to find this action, we use only the integrability condition for a differential form. The quantization of the system is reduced to the uantization of a free particle in a three-dimensional pseudo-Euclidean space. The natural measure corresponding to the CS metric is used to construct the Hermitian DeWitt and mass operators. Based on the self-consistent solution of quantum DeWitt equations and equations for the eigenvalues of the mass and charge operators, the wave function for the spherically symmetric configuration of the gravitational and electromagnetic fields in the T- region is constructed. As a result, we get a model of charged BH with continuous mass and charge spectra.

Work fluctuations in the active Ornstein–Uhlenbeck particle model

We study the large deviations of the power injected by the active force for an active Ornstein–Uhlenbeck particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in d-dimensions from a saddle-point expansion, and numerically in two dimensions by (a) direct sampling of the active work in numerical solutions of the AOUP equations and (b) Legendre–Fenchel transform of the scaled cumulant generating function obtained via a cloning algorithm. The rate function presents asymptotically linear branches on both sides and it is independent of the system’s dimensionality, apart from a multiplicative factor. For the confining potential case, we focus on two-dimensional systems and obtain the rate function numerically using both methods (a) and (b). We find a different scenario for harmonic and anharmonic potentials: in the former case, the phenomenology of fluctuations is analogous to that of a free particle, but the rate function might be non-analytic; in the latter case the rate functions are analytic, but fluctuations are realised by entirely different means, which rely strongly on the particle-potential interaction. Finally, we check the validity of a fluctuation relation for the active work distribution. In the free-particle case, the relation is satisfied with a slope proportional to the bath temperature. The same slope is found for the harmonic potential, regardless of activity, and for an anharmonic potential with low activity. In the anharmonic case with high activity, instead, we find a different slope which is equal to an effective temperature obtained from the fluctuation–dissipation theorem.

Scalable Enrichment of Immunomodulatory Human Acute Myeloid Leukemia Cell Line-Derived Extracellular Vesicles

Acute myeloid leukemia (AML) cells can secrete trophic factors, including extracellular vesicles (EVs), instructing the stromal leukemic niche. Here, we introduce a scalable workflow for purification of immunomodulatory AML-EVs to compare their phenotype and function to the parental AML cells and their secreted soluble factors. AML cell lines HL-60, KG-1, OCI-AML3, and MOLM-14 released EVs with a peak diameter of approximately 80 nm in serum-free particle-reduced medium. We enriched EVs >100x using tangential flow filtration (TFF) and separated AML-derived soluble factors and cells in parallel. EVs were characterized by electron microscopy, immunoblotting, and flow cytometry, confirming the double-membrane morphology, purity and identity. AML-EVs showed significant enrichment of immune response and leukemia-related pathways in tandem mass-tag proteomics and a significant dose-dependent inhibition of T cell proliferation, which was not observed with AML cells or their soluble factors. Furthermore, AML-EVs dose-dependently reduced NK cell lysis of third-party K-562 leukemia targets. This emphasizes the peculiar role of AML-EVs in leukemia immune escape and indicates novel EV-based targets for therapeutic interventions.

Position-dependent mass Dirac equation and local Fermi velocity

We present a new approach to study the one-dimensional Dirac equation in the background of a position-dependent mass m. Taking the Fermi velocity vf to be a local variable, we explore the resulting structure of the coupled equations and arrive at an interesting constraint of m turning out to be the inverse square of vf. We address several solvable systems that include the free particle, shifted harmonic oscillator, Coulomb and nonpolynomial potentials. In particular, in the supersymmetric quantum mechanics context, the upper partner of the effective potential yields a new form for an inverse quadratic functional choice of the Fermi velocity.

Calculation of the creation and annihilation operators of a free particle in the light cone coordinate formalism

This work didactically presents the mathematical procedures required for the construction of the creation and annihilation operators for a free quantum particle considering the coordinates of the light cone. For that, the relationships between the aforementioned coordinates and the coordinates (ct, x, y, z) are listed, in addition to the use of the Klein-Gordon-Fock equation in the formalism of the light cone coordinates. Finally, the temporal evolution operator and the quantum operators of creation and annihilation of the integral type of motion are obtained.