scholarly journals Towards Measuring the Maxwell–Boltzmann Distribution of a Single Heated Particle

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaoya Su ◽  
Alexander Fischer ◽  
Frank Cichos
Keyword(s):  
Brownian Motion ◽  
Effective Temperature ◽  
Statistical Physics ◽  
Degrees Of Freedom ◽  
Brownian Particle ◽  
Boltzmann Distribution ◽  
Heated Particle ◽  
Long Time ◽  
Inhomogeneous Temperature ◽  
Long Timescales

The Maxwell–Boltzmann distribution is a hallmark of statistical physics in thermodynamic equilibrium linking the probability density of a particle’s kinetic energies to the temperature of the system that also determines its configurational fluctuations. This unique relation is lost for Hot Brownian Motion, e.g., when the Brownian particle is constantly heated to create an inhomogeneous temperature in the surrounding liquid. While the fluctuations of the particle in this case can be described with an effective temperature, it is not unique for all degrees of freedom and suggested to be different at different timescales. In this work, we report on our progress to measure the effective temperature of Hot Brownian Motion in the ballistic regime. We have constructed an optical setup to measure the displacement of a heated Brownian particle with a temporal resolution of 10 ns giving a corresponding spatial resolution of about 23 pm for a 0.92 μm PMMA particle in water. Using a gold-coated polystyrene (AuPS) particle of 2.15 μm diameter we determine the mean squared displacement of the particle over more than six orders of magnitude in time. Our data recovers the trends for the effective temperature at long timescales, yet shows also clear effects in the region of hydrodynamic long time tails.

scholarly journals Field-Driven Brownian Motion of Magnetic Domain Walls

2010 ◽  
Vol 61 (5) ◽  
pp. 282-286
Author(s):  
Lukáš Glod ◽  
Gabriela Vasziová ◽  
Jana Tóthová ◽  
Vladimír Lisý
Keyword(s):  
Brownian Motion ◽  
Statistical Physics ◽  
Domain Walls ◽  
Brownian Particle ◽  
Mean Square Displacement ◽  
Magnetic Domain ◽  
Thermal Fluctuations ◽  
Time Correlation ◽  
Magnetic Domain Walls ◽  
Mass Position

Field-Driven Brownian Motion of Magnetic Domain WallsThe dynamics of a magnetic domain wall (DW) in a wire is studied. The DW is modeled as a Brownian particle subjected to thermal fluctuations and is characterized by the mass, position and velocity. Its motion is damped by friction, pinned by the irregularities in the material and driven by a constant force due to the external magnetic field. We have obtained the corresponding Langevin equation that contains a white-noise force. The use of an effective method taken from the statistical physics allowed us to convert this stochastic equation into an ordinary differential equation. From its solution the mean square displacement of the DW with other relevant time correlation functions and their spectral densities have been found. The electric current induced by the moving DW is also calculated.

Introduction

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
State Level ◽  
Boltzmann Distribution ◽  
Theoretical Description ◽  
Time Dependent ◽  
Nuclear Dynamics ◽  
Molecular Reaction ◽  
Oppenheimer Approximation

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized state-to-state level is discussed. The theoretical description of these reactions based on the time-dependent Schrödinger equation and the Born–Oppenheimer approximation is introduced and the resulting time-dependent Schrödinger equation describing the nuclear dynamics is discussed. The chapter concludes with a brief discussion of matter at thermal equilibrium, focusing at the Boltzmann distribution. Thus, the Boltzmann distribution for vibrational, rotational, and translational degrees of freedom is discussed and illustrated.

A perfect probe: Resonance of underdamped scaled Brownian motion

2021 ◽  
Author(s):  
Yuhui Luo ◽  
Chunhua Zeng ◽  
Baowen Li
Keyword(s):  
Brownian Motion ◽  
Single Particle ◽  
Brownian Particle ◽  
Bistable System ◽  
Velocity Autocorrelation Function ◽  
Interacting Particles ◽  
Velocity Autocorrelation ◽  
Spectrum Density ◽  
Coupling Strengths ◽  
And Diffusion

Abstract We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function (VACF) and mean squared displacement (MSD) of a single particle, we find that for the steady state, diffusions are ballistic at short times and then become normal for most of parameter regimes. However, for certain parameter regimes, both VACF and MSD suggest that the transition between superdiffusion and subdiffusion takes place at intermediate times, and diffusion becomes normal at long times. Via the power spectrum density corresponding to the transitions, we find that there exists a nontrivial resonance. For interacting particles, we find that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we theoretically propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles and for identifying cancer cells or healthy ones.

Systematic Synthesis and Applications of Novel Multi-Degree-of-Freedom Differential Systems

1992 ◽  
Author(s):  
Sridhar Kota ◽  
Srinivas Bidare
Keyword(s):  
Degrees Of Freedom ◽  
Building Blocks ◽  
Degree Of Freedom ◽  
Differential Systems ◽  
Practical Applications ◽  
Epicyclic Gear ◽  
Differential Mechanism ◽  
Long Time ◽  
Gear Trains ◽  
Drive Systems

Abstract A two-degree-of-freedom differential system has been known for a long time and is widely used in automotive drive systems. Although higher degree-of-freedom differential systems have been developed in the past based on the well-known standard differential, the number of degrees-of-freedom has been severely restricted to 2n. Using a standard differential mechanism and simple epicyclic gear trains as differential building blocks, we have developed novel whiffletree-like differential systems that can provide n-degrees of freedom, where n is any integer greater than two. Symbolic notation for representing these novel differentials is also presented. This paper presents a systematic method of deriving multi-degree-of-freedom differential systems, a three and four output differential systems and some of their practical applications.

scholarly journals On the Hamiltonian approach: Applications to geophysical flows

1998 ◽  
Vol 5 (4) ◽  
pp. 219-240 ◽  
Author(s):  
V. Goncharov ◽  
V. Pavlov
Keyword(s):  
Degrees Of Freedom ◽  
Fluid Motion ◽  
Gauge Transformations ◽  
Motion Models ◽  
Canonical Variables ◽  
Long Time ◽  
Minimum Number ◽  
Nonlinear Gauge ◽  
Hydrodynamical System ◽  
General Method

Abstract. This paper presents developments of the Harniltonian Approach to problems of fluid dynamics, and also considers some specific applications of the general method to hydrodynamical models. Nonlinear gauge transformations are found to result in a reduction to a minimum number of degrees of freedom, i.e. the number of pairs of canonically conjugated variables used in a given hydrodynamical system. It is shown that any conservative hydrodynamic model with additional fields which are in involution may be always reduced to the canonical Hamiltonian system with three degrees of freedom only. These gauge transformations are associated with the law of helicity conservation. Constraints imposed on the corresponding Clebsch representation are determined for some particular cases, such as, for example. when fluid motions develop in the absence of helicity. For a long time the process of the introduction of canonical variables into hydrodynamics has remained more of an intuitive foresight than a logical finding. The special attention is allocated to the problem of the elaboration of the corresponding regular procedure. The Harniltonian Approach is applied to geophysical models including incompressible (3D and 2D) fluid motion models in curvilinear and lagrangian coordinates. The problems of the canonical description of the Rossby waves on a rotating sphere and of the evolution of a system consisting of N singular vortices are investigated.

Introductory remarks

1990 ◽  
Vol 332 (1627) ◽  
pp. 417-418
Keyword(s):  
Probability Theory ◽  
Brownian Motion ◽  
Random Walk ◽  
Stochastic Processes ◽  
Statistical Physics ◽  
Late 19Th Century ◽  
Fields Of Study ◽  
Wide Range ◽  
Influential Paper ◽  
Telephone Traffic

Stochastic processes are systems that evolve in time probabilistically; their study is the ‘dynamics’ of probability theory as contrasted with rather more traditional ‘static’ problems. The analysis of stochastic processes has as one of its main origins late 19th century statistical physics leading in particular to studies of random walk and brownian motion (Rayleigh 1880; Einstein 1906) and via them to the very influential paper of Chandrasekhar (1943). Other strands emerge from the work of Erlang (1909) on congestion in telephone traffic and from the investigations of the early mathematical epidemiologists and actuarial scientists. There is by now a massive general theory and a wide range of special processes arising from applications in many fields of study, including those mentioned above. A relatively small part of the above work concerns techniques for the analysis of empirical data arising from such systems.

scholarly journals Thermal Fluctuations in Electric Circuits and the Brownian Motion

2010 ◽  
Vol 61 (4) ◽  
pp. 252-256 ◽  
Author(s):  
Gabriela Vasziová ◽  
Jana Tóthová ◽  
Lukáš Glod ◽  
Vladimír Lisý
Keyword(s):  
Brownian Motion ◽  
Brownian Particle ◽  
Mean Square Displacement ◽  
Thermal Fluctuations ◽  
Stochastic Equations ◽  
Thermal Bath ◽  
Current Fluctuations ◽  
Electric Circuits ◽  
The Mean ◽  
Optically Trapped

Thermal Fluctuations in Electric Circuits and the Brownian MotionIn this work we explore the mathematical correspondence between the Langevin equation that describes the motion of a Brownian particle (BP) and the equations for the time evolution of the charge in electric circuits, which are in contact with the thermal bath. The mean quadrate of the fluctuating electric charge in simple circuits and the mean square displacement of the optically trapped BP are governed by the same equations. We solve these equations using an efficient approach that allows us converting the stochastic equations to ordinary differential equations. From the obtained solutions the autocorrelation function of the current and the spectral density of the current fluctuations are found. As distinct from previous works, the inertial and memory effects are taken into account.

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