Time-dependent Potential Research Articles

High-throughput assay to simultaneously evaluate activation of CYP3A and the direct and time-dependent inhibition of CYP3A, CYP2C9, and CYP2D6 using liquid chromatography-tandem mass spectrometry

In the early stages of drug discovery, adequate evaluation of the potential drug–drug interactions (DDIs) of drug candidates is important. Several CYP3A activators are known to lead to underestimation of DDIs. These compounds affect midazolam 1'-hydroxylation but not midazolam 4-hydroxylation. We used both metabolic reactions of midazolam to evaluate the activation and inhibition of CYP3A activators simultaneously. For our CYP inhibition assay using cocktail probe substrates, simultaneous liquid chromatography-tandem mass spectrometry monitoring of 1'-hydroxymidazolam and 4-hydroxymidazolam for CYP3A was established in addition to monitoring of 4-hydroxydiclofenac and 1'-hydroxybufuralol for CYP2C9 and CYP2D6. The results of our cocktail inhibition assay were well correlated with those of a single inhibition assay, as were the estimated inhibition parameters for typical CYP3A inhibitors. In our assay, a proprietary compound that activated midazolam 1'-hydroxylation and tended to inhibit 4-hydroxylation was evaluated along with known CYP3A activators. All compounds were well characterised by comparison of the results of midazolam 1'- and 4-hydroxylation. In conclusion, our CYP cocktail inhibition assay can detect CYP3A activation and assess the direct and time-dependent inhibition potentials for CYP3A, CYP2C9, and CYP2D6. This method is expected to be very efficient in the early stages of drug discovery.

Estimates on modulation spaces for Schrödinger operators with time-dependent sub-linear vector potentials

Estimates on modulation spaces for Schrödinger operators with time-dependent sub-linear vector potentials

Gambling demon and stopping-time fluctuation relation of a Brownian particle under a time-dependent trapping potential.

A gambling demon is an external agent that can terminate a time-dependent driving protocol when a certain observable of the system exceeds a prescribed threshold. The gambling demon is examined in detail both theoretically and experimentally in a Brownian particle system under a compressing potential trap. Insight for choosing an appropriate work threshold for stopping is discussed. The energetics and the distributions of the stopping positions and stopping times are measured in simulations to gain further understanding of the process. Furthermore, the nonstationary and far-from-equilibrium stochastic process in the action of the gambling demon allows us to examine in detail some fundamental issues in stochastic thermodynamics, such as irreversibility and stopping-time fluctuation relation. Paradoxical violation of the stopping-time fluctuation relation can be reconciled in terms of the entropy production associated with fast hidden internal degrees of freedom. All the simulation or theoretical results are confirmed experimentally.

Real-time dynamics of false vacuum decay

We investigate false vacuum decay of a relativistic scalar field initialized in the metastable minimum of an asymmetric double-well potential. The transition to the true ground state is a well-defined initial-value problem in real time, which can be formulated in nonequilibrium quantum field theory on a closed time path. We employ the nonperturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion. We also compare to classical-statistical field theory simulations on a lattice in the high-temperature regime. By this, we demonstrate that the real-time decay rates are comparable to those obtained from the conventional Euclidean (bounce) approach. In general, we find that the decay rates are time dependent. For a more comprehensive description of the dynamics, we extract a time-dependent effective potential, which becomes convex during the nonequilibrium transition process. By solving the quantum evolution equations for the one- and two-point correlation functions for vacuum initial conditions, we demonstrate that quantum corrections can lead to transitions that are not captured by classical-statistical approximations. Published by the American Physical Society 2024

Stable determination of a time-dependent matrix potential for a wave equation in an infinite waveguide

Stable determination of a time-dependent matrix potential for a wave equation in an infinite waveguide

Lagrange stability for a class of impulsive Duffing equation with low regularity

We discuss the Lagrange stability for a class of impulsive Duffing equation with time-dependent polynomial potentials. More precisely, we prove that under suitable impulses, all the solutions of the impulsive Duffing equation (with low regularity in time) are bounded for all time and that there are many (positive Lebesgue measure) quasi-periodic solutions clustering at infinity.

Grazing incidence fast atom diffraction: general considerations, semiclassical perturbation theory and experimental implications.

Using semiclassical methods, an analytical approach to describe grazing incidence scattering of fast atoms (GIFAD) from surfaces is described. First, we consider a model with a surface corrugated in the scattering plane, which includes the surface normal and the incidence direction. The treatment uses a realistic, Morse potential, within a perturbation approach, and correctly reproduces the basic GIFAD phenomenology, whereby the scattering is directed primarily in the specular direction. Second, we treat the more general case of scattering from a surface corrugated in two-dimensions. Using time averaging along the direction of fast motion in the incidence direction, we derive a time dependent potential for the GIFAD scattering away from a low index direction. The results correctly describe the observation that diffraction is seen only when the scattering plane is aligned close to a low-index direction in the surface plane. For the case of helium scattering from LiF(001) we demonstrate that the resulting theoretical predictions agree well with experiment and show that the analysis provides new information on the scattering time and the length scale of the interaction. The analysis also gives insights into the validity of the axial surface channeling approximation (ASCA) and shows that within first order perturbation theory, along a low-index direction, the full 3-dimensional problem can be represented accurately by an equivalent 2-dimensional problem with a potential averaged along the third dimension. In contrast, away from low-index directions, the effective 2-dimensional potential in the projectile frame is time-dependent.

Numerical recovery of a time-dependent potential in subdiffusion *

In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian–Caputo fractional derivative in time. Theoretically, we prove a novel conditional Lipschitz stability result, and numerically, we develop an easy-to-implement fixed point iteration for recovering the unknown coefficient. In addition, we establish rigorous error bounds on the discrete approximation. These results are obtained by crucially using smoothing properties of the solution operators and suitable choice of a weighted Lp(0,T) norm. The efficiency and accuracy of the scheme are showcased on several numerical experiments in one- and two-dimensions.

Electromagnetic plasma waves in dark energy cosmology

We explore the electromagnetic wave modes that can exist in a cosmological plasma dominated by dark energy due to a cosmological constant. It is found that, in the cold and hot plasma cases, electromagnetic plasma wave modes can be found exactly. The effect of this cosmology appears as a time-dependent potential in the wave equation for the electromagnetic modes, which effectively modifies the frequency response of the plasma. This potential depends on the metric of the spacetime and on the thermodynamical properties of the plasma. For both cases, cold and hot, the solutions are found in terms of Airy and Bessel functions, respectively. When those solutions are required to have vanishing initial conditions, a discretization on the wavelengths of the electromagnetic plasma waves is imposed. Thus, only some specific wave modes can exist in this dark energy cosmology. Relaxing those conditions, we obtain other solutions that approximate to plane waves only in the very hot plasma limit.

Exploring the time-dependent regulatory potential of microRNAs in breast cancer cells treated with proteasome inhibitors

PurposeBreast cancer (BrCa) is a predominant type of cancer with a disparate molecular nature. MicroRNAs (miRNAs) have emerged as promising key players in the regulation of pathological processes in BrCa. Proteasome inhibitors (PIs) emerged as promising anticancer agents for several human malignancies, including BrCa, inhibiting the function of the proteasome. Aiming to shed light on the miRNA regulatory effect in BrCa after treatment with PIs, we used two PIs, namely bortezomib and carfilzomib.Materials and methodsFour BrCa cell lines of distinct molecular subtypes were treated with these PIs. Cell viability and IC50 concentrations were determined. Total RNA was extracted, polyadenylated, and reversely transcribed. Next, the levels of specific miRNAs with a significant role in BrCa were determined using relative quantification, and their regulatory effect was assessed.ResultsHigh heterogeneity was discovered in the levels of miRNAs in the four cell lines, after treatment. The miRNA levels fluctuate with distinct patterns, in 24, 48, or 72 hours. Interestingly, miR-1-3p, miR-421-3p, and miR-765-3p appear as key molecules, as they were found deregulated, in almost all combinations of cell lines and PIs. In the SK-BR-3 cell line, the majority of the miRNAs were significantly downregulated in treated compared to untreated cells, with miR-21-5p being the only one upregulated. Finally, various significant biological processes, molecular functions, and pathways were predicted to be affected.ConclusionsThe diversity of pathways predicted to be affected by the diversity in miRNA expression after treatment with PIs paves the way for the recognition of new regulatory axes in BrCa.

Efficient numerical description of the dynamics of interacting multispecies quantum gases

We present a highly efficient method for the numerical solution of coupled Gross–Pitaevskii equations describing the evolution dynamics of a multi-species mixture of Bose–Einstein condensates in time-dependent potentials. This method, based on a moving and expanding reference frame, compares favorably to a more standard but much more computationally expensive solution based on a frozen frame. It allows an accurate description of the long-time behavior of interacting, multi-species quantum mixtures including the challenging problem of long free expansions relevant to microgravity and space experiments. We demonstrate a successful comparison to experimental measurements of a binary Rb–K mixture recently performed with the payload of a sounding rocket experiment.

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.

An inverse problem of identifying the time-dependent potential and source terms in a two-dimensional parabolic equation

In this article, simultaneous identification of the time-dependent lowest and source terms in a two-dimensional (2D) parabolic equation from knowledge of additional measurements is studied. Existence and uniqueness of the solution is proved by means of the contraction mapping on a small time interval. Since the governing equation is yet ill-posed (very slight errors in the time-average temperature input may cause relatively significant errors in the output potential and source terms), we need to regularize the solution. Therefore, regularization is needed for the retrieval of unknown terms. The 2D problem is discretized using the alternating direction explicit (ADE) method and reshaped as non-linear least-squares optimization of the Tikhonov regularization function. This is numerically solved by means of the MATLAB subroutine $lsqnonlin$ tool. Finally, we present a numerical example to demonstrate the accuracy and efficiency of the proposed method. Our numerical results show that the ADE is an efficient and unconditionally stable scheme for reconstructing the potential and source coefficients from minimal data which makes the solution of the inverse problem (IP) unique.

Formation, propagation, and excitation of matter solitons and rogue waves in chiral BECs with a current nonlinearity trapped in external potentials.

In this paper, we investigate formation and propagation of matter solitons and rogue waves (RWs) in chiral Bose-Einstein condensates modulated by different external potentials, modeled by the chiral Gross-Pitaevskii (GP) equation with the current nonlinearity and external potentials. On the one hand, the introduction of two potentials (Pöschl-Teller and harmonic-Gaussian potentials) enables the discovery of exact soliton solutions in both focusing and defocusing cases. We analyze the interplay effects of current nonlinearity and potential on soliton stability via associated Bogoliubov-de Gennes equations. Moreover, multiple families of numerical solitons (ground-state and dipole modes) trapped in potentials are found, exhibiting distinctive structures. The interactions between solitons trapped in potentials are studied, which exhibit the inelastic trajectories and repulsive interactions. On the other hand, we introduce the time-dependent potentials such that the controlled RWs are found in both focusing and defocusing GP equations with current nonlinearity. Furthermore, through the interaction between potentials and current nonlinearity, it is possible to enlarge the region of modulational instability, leading to the generation of RWs and chiral solitons. High-order RWs are generated from several Gaussian perturbations on a continuous wave. The presence of current nonlinearity disrupts the structures of these high-order RWs, causing them to undergo a transform into chiral lower-amplitude solitons. Finally, various types of soliton excitations are investigated by varying the strengths of potential and current nonlinearity, showing the abundant dynamic transforms of chrital matter solitons.

Simulations and theory of power spectral density functions for time-dependent and anharmonic Langevin oscillators.

Simulations and theory are presented for the power spectral density functions (PSDs) of particles in time-dependent and anharmonic potentials, including the effects of a thermal environment leading to damping and fluctuating forces. We investigate three one-dimensional perturbations to the harmonic oscillator of which two are time-dependent changes in the natural frequency of the oscillator, while the other is a time-independent extension of the quadratic potential to include a quartic term. We investigate the effect of these perturbations on two PSDs of the motion that are used in experiments on trapped nano-oscillators. We also derive and numerically test the PSDs for the motion of a spherical nanoparticle in a Paul trap. We found that the simple harmonic Langevin oscillator's PSDs are good approximations for the x and y coordinates' PSDs for small values of the parameter q of the Mathieu equation, but the difference can be more than a factor of two as "q" increases. We also numerically showed that the presence of a permanent electric dipole on the nanosphere can significantly affect the PSDs in the x and y coordinates.

Nonlinear gain models in a quantum cascade laser.

Density matrix analysis of a three-state model of quantum cascade laser (QCL) reveals that in this device, the optical gain is composed of the linear part (proportional to population inversion Δn) and the remaining nonlinear part. The nonlinear component non-negligibly contributes even to the small-signal response of the medium. In many attempts to modeling QCLs, the common practice to account for nonlinear gain components is to complement the equation for the gain, g = gcΔn, gc is the gain cross-section, by a compression factor f. In this paper, improved (but still simple) models of the optical gain in QCL are proposed, which preserve the two-component gain structure. With these models, there is no need to solve the Hamiltonian with time-dependent potentials, so that extraordinary numerical loads can be avoided, but simultaneously the essential physics of the phenomena is kept. The improved gain models defined by Eqs.(12), (15) and (16) enable accounting for its nonlinear components while preserving the load-saving, scattering-like approach to light-matter interaction. It is also shown that as long as the populations and dc coherences are determined such that they account for the interaction with the optical field, the small-signal formulation of the gain gives its realistic estimate also for a large optical signal. This conjecture validates the use of non-equilibrium Green's function-based approaches, in which the interaction with the optical field is included through electron-photon selfenergies. The small-signal formulation of the gain can be used in this approach to monitor the saturation process, estimate the clamping flux and the light-current characteristic.

Ballistic dynamics of emergent soliton from Airy pulse in a medium with linear optical potential

We numerically investigate the propagation dynamics of Airy pulse in dispersive and nonlinear medium with time-dependent external optical potential. These time-dependent optical potentials are created by the co-propagating strong pump wave. In the presence of linear optical potential, soliton shedding from signal Airy pulse is observed, which demonstrates ballistic motion. However, emergent soliton can either be advanced or delayed depending upon the sign of the potential and the extent of temporal advancement or delay is directly proportional to the magnitude of the potential strength. In addition, the temporal shift of the emergent soliton is found to be dependent on the input pulse power. Moreover, we show ballistic motion of the emergent soliton by incorporating an initial linear phase as well as linear chirp (quadratic phase) parameters in the input Airy pulse. Furthermore, the effect of truncation factor on the propagation dynamics is explored. These results provide new insights on the manipulation of the signal Airy pulse dynamics in dispersive and nonlinear media.

Evolution of the wave function's shape in a time-dependent harmonic potential

Abstract An effective operational approach to quantum mechanics is to focus on the evolution of wave packets, for which the wave function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of freedom describing the shape of the wave packet and its fluctuations. These quantum dressing are independent degrees of freedom, mathematically encoded in the higher moments of the wave function. We review how to extract the effective dynamics for Gaussian wave packets evolving according to the Schrödinger equation with time-dependent potential in a 1 + 1-dimensional spacetime, and derive the equations of motion for the quadratic uncertainty. We then show how to integrate the evolution of all the higher moments for a general wave function in a time-dependent harmonic potential.

Hölder stability estimates in determining the time-dependent coefficients of the heat equation from the Cauchy data set

Abstract In this paper, we address stability results in determining the time-dependent scalar and vector potentials appearing in the convection-diffusion equation from the knowledge of the Cauchy data set. We prove Hölder-type stability estimates. The key tool used in this work is the geometric optics solution.

Optimal performance of the stochastic thermodynamic engine with a periodic heat bath

Stochastic thermodynamics provides a conceptual framework for describing the fluctuating behavior of small systems like colloids or biomolecules far from thermodynamic equilibriums but still contacted with a heat bath. In contrast to most literature focusing on the classical paradigm of Carnot engines, we herein study the optimal performance of the thermodynamic heat engine with a heat bath that periodically changes temperature, which is outside controllable by a time-dependent harmonic potential. Under reasonable assumptions on the control actuation, we derive the achievable upper bound for the maximal power and also the optimal control protocol. In addition, we also obtain the corresponding efficiency at maximal power, which only depends on the ratio of the minimal and maximal value of the temperature profile.