Free particle

In physics, a free particle is a particle that, in some sense, is not bound by an external force, or equivalently not in a region where its potential energy varies. In classical physics, this means the particle is present in a "field-free" space. In quantum mechanics, it means the particle is in a region of uniform potential, usually set to zero in the region of interest since the potential can be arbitrarily set to zero at any point in space. Classical free particle The classical free particle is characterized by a fixed velocity v. The momentum is given by \mathbf{p}=m\mathbf{v} and the kinetic energy (equal to total energy) by E=\frac{1}{2}mv^2=\frac{p^2}{2m} where m is the mass of the particle and v is the vector velocity of the particle. Quantum free particle Mathematical description Schrödinger equation and Matter wave A free particle with mass m in non-relativistic quantum me

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Publications associées (3)

Publications associées

Chargement

Personnes associées

Chargement

Unités associées

Chargement

Concepts associés (12)

Concepts associés

Chargement

Cours associés (28)

Cours associés

Chargement

Séances de cours associées (59)

Afficher plus

Séances de cours associées

Chargement

Work fluctuations in the active Ornstein-Uhlenbeck particle model

Francesco Cagnetta

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.

IOP Publishing Ltd2021

Chargement

Spin Polarization and Attosecond Time Delay in Photoemission from Spin Degenerate States of Solids

Jan Hugo Dil, Mauro Fanciulli, Stefan Peter Muff

After photon absorption, electrons from a dispersive band of a solid require a finite time in the photoemission process before being photoemitted as free particles, in line with recent attosecond-resolved photoemission experiments. According to the Eisenbud-Wigner-Smith model, the time delay is due to a phase shift of different transitions that occur in the process. Such a phase shift is also at the origin of the angular dependent spin polarization of the photoelectron beam, observable in spin degenerate systems without angular momentum transfer by the incident photon. We propose a semiquantitative model which permits us to relate spin and time scales in photoemission from condensed matter targets and to better understand spin-and angle-resolved photoemission spectroscopy (SARPES) experiments on spin degenerate systems. We also present the first experimental determination by SARPES of this time delay in a dispersive band, which is found to be greater than 26 as for electrons emitted from the sp-bulk band of the model system Cu(111).

American Physical Society2017

Chargement

The Geometry of Eye Movement Dynamics

Simon Nessim Henein, Ilan Vardi

Eye movements consist of spherical rotations, with orientation generally constrained by Listing’s law. Our main result is a complete explicit formulation of ballistic eye movement under the Listing constraint. We present a conceptual framework for eye movement bas-ing the dynamics of Listing motion on the equator of the sphere of unit quaternions, which we call the Listing sphere. Analytical dynamics shows that ballistic Listing motion corre-sponds to free particle motion on the Listing sphere. Thus, ballistic Listing movement is greatly simplified by transposition to the Listing sphere, where it consists of shortest dis-tance trajectories. This proves that ballistic eye motion consists of constant speed rotation along circles passing through the occipital point. The relevance of the occipital point in eye movement was already noted by Helmholtz, which we explain by the fact that it cor-responds to the equator of the Listing sphere. We designed a physical mechanism produc-ing the correspondence between eye movement and particle motion on the Listing sphere. Our straightforward description of ballistic eye motion under the pure Listing kinematic constraint serves as a useful idealized benchmark in the study of actual physiological eye movements, whose orientations are known to deviate slightly from the Listing constraint.

2015

Chargement

Fonction d'onde

thumb|300px|right|Illustration de la notion de fonction d'onde dans le cas d'un oscillateur harmonique. Le comportement en mécanique classique est représenté sur les images A et B et celui en mécaniqu

Principe d'incertitude

En mécanique quantique, le principe d'incertitude ou, plus correctement, principe d'indétermination, aussi connu sous le nom de principe d'incertitude de Heisenberg, désigne toute inégalité mathémat

Amplitude de probabilité

vignette|Une fonction d'onde pour un seul électron dans l'orbite atomique 5d d'un atome d'hydrogène . La forme montre les endroits où la densité de probabilité de l'électron est supérieure à une certa

PHYS-426: Quantum physics IV

Introduction to the path integral formulation of quantum mechanics. Derivation of the perturbation expansion of Green's functions in terms of Feynman diagrams. Several applications will be presented, including non-perturbative effects, such as tunneling and instantons.

PHYS-425: Quantum physics III

To introduce several advanced topics in quantum physics, including semiclassical approximation, path integral, scattering theory, and relativistic quantum mechanics

ME-469: Nano-scale heat transfer

In this course we study heat transfer (and energy conversion) from a microscopic perspective. This allows us to understand why classical laws (i.e. Fourier Law) are what they are and what are their limits of validity . We will then discuss emerging opprotunities in nanoscale devices.