Metastable Potential Research Articles

Quantifying the energy landscape in weakly and strongly disordered frictional media.

We investigate the "roughness" of the energy landscape of a system that diffuses in a heterogeneous medium with a random position-dependent friction coefficient α(x). This random friction acting on the system stems from spatial inhomogeneity in the surrounding medium and is modeled using the generalized Caldira-Leggett model. For a weakly disordered medium exhibiting a Gaussian random diffusivity D(x) = kBT/α(x) characterized by its average value ⟨D(x)⟩ and a pair-correlation function ⟨D(x1)D(x2)⟩, we find that the renormalized intrinsic diffusion coefficient is lower than the average one due to the fluctuations in diffusivity. The induced weak internal friction leads to increased roughness in the energy landscape. When applying this idea to diffusive motion in liquid water, the dissociation energy for a hydrogen bond gradually approaches experimental findings as fluctuation parameters increase. Conversely, for a strongly disordered medium (i.e., ultrafast-folding proteins), the energy landscape ranges from a few to a few kcal/mol, depending on the strength of the disorder. By fitting protein folding dynamics to the escape process from a metastable potential, the decreased escape rate conceptualizes the role of strong internal friction. Studying the energy landscape in complex systems is helpful because it has implications for the dynamics of biological, soft, and active matter systems.

Irregular pitting propagation within the inclusions in Ce-doped Fe40Mn20Cr20Ni20 high-entropy alloy

Comprehensive investigations on the impact of Ce doping on the pitting resistance of Fe40Mn20Cr20Ni20 high-entropy alloys in 3.5% NaCl solution were conducted with an emphasis on the inclusions involved. The correlation between the variations of the type, number and size of inclusions and the doping of Ce were identified. The increased pitting resistance of the alloy induced by the doping of Ce was found associated with higher metastable pitting potentials and steady-state pitting potentials. The morphology evolution with the inclusions captured by SEM images and EDS mapping strongly indicated an existence a double-layer structure in Ce-doped Fe40Mn20Cr20Ni20 high-entropy alloys. An evident irregular pitting propagation path was probed in Ce-doped samples.

Reactive flux theory for finite potential barriers and memory friction

The reactive flux theory for finite barriers that we proposed in a previous work is generalized to memory friction. For an internal colored noise, the steady-state probability density dose not exist for some noise parameters, whose role can be replaced by an effective steady-state probability density. The theoretical method is illustrated by a Brownian particle moving in a metastable potential and subjected to an internal Ornstein–Uhlenbeck noise. The theoretical results agree well with the Langevin simulation results in the spatial diffusion regime until relatively low potential barrier heights. The Arrhenius law is examined at low barrier heights.

Pensare l’intrusione: Merleau-Ponty face à gaia

The expression “ecological threat” refers to a dynamic of double intrusion: the intrusion of geological history in human history (the intrusion of Gaia) and the intrusion of human history in geological history (the Anthropocene). This double intrusion is founded on a series of major partitions (culture/nature; society/environment) that do not allow for the possibility of communication between the terms of these dichotomies unless it is in the form of reciprocal violation. In the article, the ontology of the flesh is used in order to think the intrusion in a different way compared to the great partitions. Within a chiasmatic logic, the terms of each dichotomy are understood as inseparable moments of the same flesh which institutes a difference – inside/outside – through an infinite movement of folding and torsion. By thinking this common element, Merleau-Ponty’s ontology of the flesh enters in dialogue with Amerindian mythocosmologies of the “first Anthropocene.” In these mythocosmologies, a humanity-flesh – understood as a transformative, pre-individual, and metastable potential – gives birth, through differentiation, to the multiple points of view that populate the cosmos. This dialogue allows us to think about the socialization of Gaia and to trace the contours of a general ecology understood as a thought that operates between – or beyond – major partitions.

Simondoniana

Kodalak’s essay revisits Gilbert Simondon as a postwar philosopher, who formulated a new way of conceiving individual modalities—from crystals, technical objects and biological organisms to psychic phenomena and social collectives. Simondon’s metaphysical conception of ontogenesis—that explains how individuals emerge from a pre-individual field of metastable potentials through processes of individuation—helped him reconceive technical objects, no longer as passive automata, but as exuberant individuals, active and full of life, with irreducible modes of existence of their own. With this new vision, Simondon invites us to rethink our relationship with technical objects beyond the mythological attitudes of technocracy, technophilia, and technophobia, which can be further developed today for reconceiving architecture’s own technical modes of existence and charged relations with technology. Kousoulas’ essay begs the question: Why Simondon in a volume dedicated to Stiegler? It is not that Stiegler’s oeuvre cannot be examined without referring to the crucial influence that Simondon had for his thought. More important than this, it is only through Simondon that Stiegler makes sense. Simondon is keen to remind us that sense, first and foremost, stands for directionality: to make sense is to grasp a direction. Without Simondon’s critical reformulation of our technological becoming, Stiegler’s project remains null. In a non-zero-sum game, Stiegler through Simondon and (retroactively) Simondon through Stiegler, produce the norms and values of a directing sense that can indeed compel us to engage in our worldly endeavours with neganthropic care.

Monte Carlo study of transport in low-dimensional quantum disorder systems at finite temperature

Using the quantum generalized Langevin equation and the path integral Monte Carlo approach, we study the transport dynamics of low-dimensional quantum disorder systems at finite temperature. Motivated by the nature of the classical-to-quantum transformation in fluctuations in the time domain, we extend the treatment to the spatial domain and propose a quantum random-correlated potential, describing specifically quantum disorder. For understanding the Anderson localization from the particle transport perspective, we present an intuitive treatment using a classical analogy in which the particle moves through a flat periodic crystal lattice corrugated by classical or quantum disorder. We emphasize an effective classical disorder potential in studying the quantum effects on the transport dynamics. Compared with the classical case, we find that the quantum escape rate from a disordered metastable potential is larger. Moreover, the diffusion enhancement of a quantum system moving in a weak, biased, periodic disorder potential is more significant compared with the classical case; for an effective rock-ratcheted disorder potential, quantum effects increase the directed current with decreasing temperature. For the classical case, we explore surface diffusion on a two-dimensional biased disorder potential at finite temperature; surprisingly, the optimal angle of the external bias force is found to enhance diffusion in the biased disorder surface. Furthermore, to explain the quantum transport dynamics in a disorder potential, we adopt the barrier-crossing mechanism and the mean first passage time theory to establish the probability distribution function.

Exponential speedup of incoherent tunneling via dissipation

We study the escape rate of a particle in a metastable potential in presence of a dissipative bath coupled to the momentum of the particle. Using the semiclassical bounce technique, we find that this rate is exponentially enhanced. In particular, the influence of momentum dissipation depends on the slope of the barrier that the particle is tunneling through. We investigate also the influence of dissipative baths coupled to the position, and to the momentum of the particle, respectively. In this case the rate exhibits a non-monotonic behavior as a function of the dissipative coupling strengths. Remarkably, even in presence of position dissipation, momentum dissipation can enhance exponentially the escape rate in a large range of the parameter space. The influence of the momentum dissipation is also witnessed by the substantial increase of the average energy loss during inelastic (environment-assisted) tunneling.

Reactive flux theory for finite potential barriers.

Motivated by developing a simple, accurate, and widely applicable approach to incorporate the finite barrier correction in analytical calculation of the escape rate, the reactive flux theory for finite barriers is proposed. For higher temperatures, instead of at the top of the barrier in the original reactive flux theory, the starting point of the trajectories of Brownian particles is removed into a position inside the potential well where the probability distribution can be regarded as an equilibrium one, and the potential barrier is replaced with an equivalent parabolic potential barrier. The equivalent potential barrier frequency can be obtained by two schemes. The population is also calculated more realistically for finite barriers. The theoretical method is tested by a Brownian particle moving in a cubic metastable potential and subjected to Gaussian white noise. The numerical simulation results confirm the approach satisfactorily until lower reduced barrier heights.

The effective potential originating from swampland and the non-trivial Brans-Dicke coupling * * Supported by the National Natural Science Foundation of China (11775080, 11865016)

The effective vacuum energy density contributed by the non-trivial contortion distribution and the bare vacuum energy density can be viewed as the energy density of the auxiliary quintessence field potential. We find that the negative bare vacuum energy density from string landscape leads to a monotonically decreasing quintessence potential while the positive one from swampland leads to the metastable or stable de Sitter-like potential. Moreover, the non-trivial Brans-Dicke like coupling between the quintessence field and gravitation field is necessary in the latter case.

Effect of Self-Oscillation on Escape Dynamics of Classical and Quantum Open Systems.

We study the effect of self-oscillation on the escape dynamics of classical and quantum open systems by employing the system-plus-environment-plus-interaction model. For a damped free particle (system) with memory kernel function expressed by Zwanzig (J. Stat. Phys. 9, 215 (1973)), which is originated from a harmonic oscillator bath (environment) of Debye type with cut-off frequency , ergodicity breakdown is found because the velocity autocorrelation function oscillates in cosine function for asymptotic time. The steady escape rate of such a self-oscillated system from a metastable potential exhibits nonmonotonic dependence on , which denotes that there is an optimal cut-off frequency makes it maximal. Comparing results in classical and quantum regimes, the steady escape rate of a quantum open system reduces to a classical one with decreasing gradually, and quantum fluctuation indeed enhances the steady escape rate. The effect of a finite number of uncoupled harmonic oscillators N on the escape dynamics of a classical open system is also discussed.

Staying dynamics: An approach to solve the inverse Kramers problem

The inverse Kramers problem, i.e., a particle passing over the barrier of a metastable potential and then escaping from the potential well, can be applied to model many subjects such as nuclear and atom cluster fusions, molecular collision. We consider the metastable potential to be a parabolic potential linking smoothly with a harmonic potential, thus the staying dynamics of a particle in the metastable potential well is investigated semi-analytically. The analytical expression of time-dependent staying probability is obtained through a coarse graining scheme for the particle multi-passing process over the joint point of potentials. A combination of the Kramers rate formula for intermediate to long times with our theoretical results is in well agreement with the Langevin simulations. The staying probability at the crossover between our result and the Kramers formula may be used to improve the calculation of the fusion probability in superheavy nuclei synthesis.

Anomalous Dynamics of Inertial Systems Driven by Colored Lévy Noise

Dynamics of underdamped particles subjected to colored Levy noise is investigated analytically. The probability density distribution of the Levy particle in the harmonic potential is exactly obtained by solving the fractional Fokker–Planck equation, which is also a Levy type one with width depends on both correlation time $$\tau _c$$ and damping coefficient $$\gamma $$ and converges to the distribution for the white-noise, overdamped case in the limit $$\tau _c\rightarrow 0$$ , $$\gamma \rightarrow \infty $$ . Moreover, we obtain an analytical expression of escape rate for the underdamped particle escaping from a metastable potential by using the reactive flux method. It is shown that the stationary escape rate exhibits nonmonotonic dependence on the Levy index, while an increase of the noise correlation time leads to the monotonic decrease of escape rete.

Diffusion crossing over a barrier in a random rough metastable potential.

We carry out a detailed study of escape dynamics of a particle driven by a white noise over a metastable potential corrugated by spatial disorder in the form of zero-mean random correlated potential. The approach of double-averaging over test particles and statistic ensemble is proposed to calculate the escape rate in a finite-size random rough metastable potential, moreover, the interference mechanism of test particles multi-passing over the saddle point is considered. Through analyzing the dependence of the steady escape rate on various modelled potentials and parameters, we demonstrate that the obstruction induced by roughness leads to a decrease in the steady escape rate with the increase of rough intensity. We also add the random correlated potential into the vicinity of the saddle-point of metastable potentials of three kinds and show an enhancement phenomenon of escape rate similar to the previous study of a surmounting fluctuating sharp barrier.

Entangled trajectories Hamiltonian dynamics for treating quantum nuclear effects.

A simple and robust methodology, dubbed Entangled Trajectories Hamiltonian Dynamics (ETHD), is developed to capture quantum nuclear effects such as tunneling and zero-point energy through the coupling of multiple classical trajectories. The approach reformulates the classically mapped second-order Quantized Hamiltonian Dynamics (QHD-2) in terms of coupled classical trajectories. The method partially enforces the uncertainty principle and facilitates tunneling. The applicability of the method is demonstrated by studying the dynamics in symmetric double well and cubic metastable state potentials. The methodology is validated using exact quantum simulations and is compared to QHD-2. We illustrate its relationship to the rigorous Bohmian quantum potential approach, from which ETHD can be derived. Our simulations show a remarkable agreement of the ETHD calculation with the quantum results, suggesting that ETHD may be a simple and inexpensive way of including quantum nuclear effects in molecular dynamics simulations.

Anomalous diffusion resulted from fractional damping

The dynamics of a Brownian particle diffusing in the pure fractional damping environment is studied in the field of a metastable potential. Several anomalous behaviors are revealed such as that a type of reverse diffusion is encountered. And the diffusion dynamics is closely related to the fractional exponent α. Particles are found to move reversely in the opposite direction of diffusion when α is relatively large despite of the zero-approximating effective friction of the system

Non-Markovian Lévy dynamics and the effect of the underlying time correlation

The combined effect of symmetric α-stable Lévy flights and their underlying time correlations, namely, non-Markovian Lévy dynamics, is studied. By the use of the propagation function approach, which allows in a natural way for the inclusion of ‘correlated’ Lévy noise, we derive a version of the apparent width for the Lévy distribution. The correlated Lévy flights in the absence of nonlinearity are described by integral forms of coupling Langevin equations. Using a Monte-Carlo simulation of the motion of a particle in a metastable potential, we show the interfering phenomenon of the escape process. Finally, we expand the model to a Lévy-type random environment, i.e. a particle is coupled to a set of finite independent oscillators obeying the symmetric α-stable Lévy distributions. Thus, a non-thermalization generalized Langevin equation is proposed, where the fluctuation-dissipation theorem does not hold, which exhibits ballistic diffusion for any α. A numerical solution for Hamilton’s equations of motion with the initial random data confirms the present theoretical finding.

Anomalous barrier escape: The roles of noise distribution and correlation.

We study numerically and analytically the barrier escape dynamics of a particle driven by an underlying correlated Lévy noise for a smooth metastable potential. A "quasi-monochrome-color" Lévy noise, i.e., the first-order derivative variable of a linear second-order differential equation subjected to a symmetric α-stable white Lévy noise, also called the harmonic velocity Lévy noise, is proposed. Note that the time-integral of the noise Green function of this kind is equal to zero. This leads to the existence of underlying negative time correlation and implies that a step in one direction is likely followed by a step in the other direction. By using the noise of this kind as a driving source, we discuss the competition between long flights and underlying negative correlations in the metastable dynamics. The quite rich behaviors in the parameter space including an optimum α for the stationary escape rate have been found. Remarkably, slow diffusion does not decrease the stationary rate while a negative correlation increases net escape. An approximate expression for the Lévy-Kramers rate is obtained to support the numerically observed dependencies.

Local discretization method for overdamped Brownian motion on a potential with multiple deep wells.

We present a general method for transforming the continuous diffusion equation describing overdamped Brownian motion on a time-independent potential with multiple deep wells to a discrete master equation. The method is based on an expansion in localized basis states of local metastable potentials that match the full potential in the region of each potential well. Unlike previous basis methods for discretizing Brownian motion on a potential, this approach is valid for periodic potentials with varying multiple deep wells per period and can also be applied to nonperiodic systems. We apply the method to a range of potentials and find that potential wells that are deep compared to five times the thermal energy can be associated with a discrete localized state while shallower wells are better incorporated into the local metastable potentials of neighboring deep potential wells.

Critical scaling in the large-NO(N)model in higher dimensions and its possible connection to quantum gravity

The critical scaling of the large-$N$ $O(N)$ model in higher dimensions using the exact renormalization group equations has been studied, motivated by the recently found non-trivial fixed point in $4<d<6$ dimensions with metastable critical potential. Particular attention is paid to the case of $d=5$ where the scaling exponent $\nu$ has the value $1/3$, which coincides with the scaling exponent of quantum gravity in one fewer dimensions. Convincing results show that this relation could be generalized to arbitrary number of dimensions above five. Some aspects of AdS/CFT correspondence are also discussed.

Modified fusion probability by reflection boundary**Supported by National Natural Science Foundation of China (11175021) and Specialized Research Fund for the Doctoral Program of Higher Education (20120003110025)

We investigate the time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to the whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of an inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of the reflection boundary of the potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability of passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of the passing probability over the saddle point of an inverse harmonic potential.