arXiv subjects

Pedro J. Colmenares

Publications and source records attributed to Pedro J. Colmenares.

11 recordsLinked to original sources

arXiv2026

Velocity modulus diffusion of self-propelled spherical and circular particles: A generalized Langevin approach

This research presents a framework for describing the average velocity magnitude of an accelerated, self-propelled Brownian particle diffusing in a thermal fluid and confined by a harmonic external potential. The system is immersed in a thermal bath of harmonic oscillators at a constant temperature, where the bath constituents also interact with the external field. The dynamics are investigated for both a sphere and a disk, partitioned into two distinct stochastic processes. The first process describes the coarse-grained, time-dependent internal self-velocity generated by a set of independent Ornstein-Uhlenbeck processes, independent of the external field. This internal mechanism provides the initial velocity for the particle to diffuse within the fluid, which is modeled via a modified generalized Langevin equation as the second process. We find that the system exhibits spontaneous fluctuations in the diffusive velocity magnitude due to the internal mechanism; however, as expected, these momentary fluctuations decay at long times. Finally, the internal propulsion velocity magnitude in spherical coordinates is derived, accompanied by simulations of the different magnitudes for both the sphere and the disk, the latter following established equations in polar coordinates.

cond-mat.stat-mech↗

arXiv2026

Adiabatic protocol for the generalized Langevin equation

This article proposes a self-consistent methodology for determining the mechanical adiabatic work of Brownian particles trapped in optical tweezers. Rather than varying the trap frequency, the proposed protocol involves displacing the trap according to a predefined schedule. Assuming the dynamics obey a modified generalized Langevin equation previously introduced by the author, we find that the external driving depends on the system's dynamical properties and, in contrast to isothermal processes, does not require external optimization. The model is fully characterized by its intrinsic parameters, requiring no additional variables. Furthermore, it is shown that along the particle trajectory, the protocol must be optimized and expressed as an integral equation.

cond-mat.stat-mech↗

arXiv2023

Generalized optimal protocols of Brownian motion in a parabolic potentia

The generalized Langevin equation with an exponential kernel is used to analyze memory effects on the optimal work done by a Brownian particle in a heat bath and subjected to a harmonic moving potential. The generalized overdamping scenario is also investigated. Several facts emerge in these more precise descriptions using the same initial conditions of the Markovian which lead the particle to do mechanical work against the field. Compared with the results obtained with the latter, the memory fades the discontinuities observed in the highly underdamped regime, which suggests that this trait is a consequence of the Markov approximation as well as the dependence of the different dynamical susceptibilities with the external field. Unlike the overdamped Markovian, work is done by the external field in the analog generalized counterpart. A detailed calculation of the rate of entropy production gives negative values. It is mathematically correct because the dynamics deal with a reduced description of the degrees of freedom of the bath. The theory then requires improving the treatment of them to restore the second law and thus to get the results with the required thermodynamics consistency.

cond-mat.stat-mech↗

arXiv2023

Optimal work of Brownian motion in a harmonic time-dependent stiffness potential. Effect of the initial position

The system consists of a Brownian particle immersed in a heat bath trapped in optical tweezers with a time-dependent strength acting as an external protocol. In [Phys. Rev. Letts., 98:108301, 2007] the optimal mean work in the overdamped regime was thoroughly calculated by assuming the work must be averaged over the distribution of the initial position of the particle. The present research assumes instead the solution of the Langevin equation for any given initial position and its average done over the noise distribution. Therefore, this proposal extends in a more general sense the results already published, including the appearance of Maxwell's demon for particular initial conditions which is analyzed in terms of entropy production rate and the mutual information obtained by measuring the particle position. The proposed research has the advantage of being able to be compared with data from numerical simulations.

cond-mat.stat-mech↗

arXiv2020

Susceptibility of quasiclassical Brownian motion in harmonic nonlinear potentials

This work sets the exact equations for the quasiclassical response function and susceptibility of a Brownian particle immersed in a bath of quantum harmonic oscillators driving by nonlinear harmonic potentials. A delta force perturbation gives rise to a response whose susceptibility is the combination of a linear term, own of the harmonic oscillator, plus a nonlinear one involving an integral \textcolor{black}{equation. It is provided a recursion method to find its solutions based on functional equations in the Banach space.} The ODE for the response function is a highly nonlinear damped non-autonomous Duffing equation for which the aforementioned method is used to get its solution.

quant-ph↗

arXiv2019

Generalized diffusion of quantum Brownian motion

This article discusses the numerical result predicted by the quantum Langevin equation of the generalized diffusion function of a Brownian particle immersed in an Ohmic quantum bath of harmonic oscillators. The time dependence of the standard deviation of the reduced Wiener function of the system, obtained by integrating the whole function in the momentum space, is determined as well. The complexity of the equations leads to resort to a much simpler calculation based in the position correlation function. They are done for the three possible regimes of the system, namely, periodic, aperiodic and overdamped. It is found in the periodic case that the generalized diffusion is a discontinuous function exhibiting negative values during short time periods of time. This counterintuitive result, found theoretically in other systems and waiting for its experimental confirmation, can be perfectly explained in the framework of the quantum Langevin equation. Its oscillatory behavior is primordially due to the response to the external field while its quantum origin contributes only in its magnitude. The results are compared with those of the continuum limit which exhibits similar behavior.

quant-ph↗

arXiv2019

Thermodynamic work associated to quantum Brownian motion in an external field

This work focuses on the response to an external field of a Brownian particle submerged in an Ohmic quantum thermal bath. The field only affects the dynamics of the central particle without affecting the thermal reservoir. The thermodynamic function to be analyzed is the average work due only to the external force. Being energy a non-local function of the protocol, a standard variational principle is used to derive it. It was found that the energy reaches a minimum imposing a restriction on the optimal protocol. This is found by applying the variational principle to the non-local work functional.It is also a minimum and only depends of the friction coefficient of the surrounding fluid.

quant-ph↗

arXiv2018

Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

This article has to do with the derivation and solution of the Fokker--Planck equation associated to the momentum-independent Wigner function, of a particle subjected to a harmonic external field and immersed in a ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung and Grabert of interpreting the operators as c-numbers to derive the adjoint equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm and Ingold. By means of a single Wigner transformation, it is found a simpler master quantum equation than that of mentioned before. The Wigner function reproduces the known results of the classical limit. This allowed to rewrite the underdamped classical Langevin equation as a first order stochastic differential equation with time-dependent drift and diffusion terms.

quant-ph↗

arXiv2016

Extracting work from a single reservoir in the non-Markovian underdamped regime

We derive optimal-work finite time protocols for a colloidal particle in a Gaussian well in the general non-Markovian underdamped regime in contact with a single reservoir. Optimal work protocols with and without measurements of position and velocity are shown to be linear in time. In order to treat the underdamped regime one must address forcing the particle at the start and at the end of a protocol, conditions which dominate the short time behaviour of the colloidal particle. We find that for protocols without measurement the least work by an external agent decreases linearly for forced start-stop conditions while those only forced at starting conditions are quadratic (slower) at short times, while both decrease asymptotically to zero for quais-static processes. When measurements are performed protocols with start-end forcing are still more efficient at short times but can be overtaken by start-only protocols at a threshold time. Measurement protocols derive work from the reservoir but always below the predicted by the Sagawa's generalization of the second law. Velocity measurement protocols are more efficient in deriving work than position measurements.

cond-mat.stat-mech↗

arXiv2016

The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

The non--static generalized Langevin equation and its corresponding Fokker--Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external force was obtained analytically. The non--Markovian stochastic differential equation, associated to the dynamics of the position under a colored noise, was then applied to the description of the dynamics and persistence time of particles constrained within absorbing barriers. Comparisons with molecular dynamics were very satisfactory.

cond-mat.stat-mech↗

arXiv2011

On the Scaling of Langevin and Molecular Dynamics Persistence Times of Non-Homogeneous Fluids

The solution of the Langevin equation of an anisotropic fluid [Colmenares P. J; López F. and Olivares-Rivas W., Phys. Rev E. 2009, 80061123] allowed the evaluation of the position dependent perpendicular and parallel diffusion coefficients, using Molecular Dynamics data. However, the time scale of the Langevin Dynamics and Molecular Dynamics are different and an anzat for the persistence probability relaxation time was needed. Here we show how the solution for the average persistence probability obtained from the Smoluchowski-Fokker-Planck equation (SE), associated to the Langevin Dynamics, scales with the corresponding Molecular Dynamics quantity. Our SE perpendicular persistence time is evaluated in terms of simple integrals over the equilibrium local density. When properly scaled by the perpendicular diffusion coefficient, it gives a good match with that obtained from Molecular Dynamics.

cond-mat.stat-mech↗