Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2307.13276 · American Journal of Physics

Force on a moving object in an ideal quantum gas

Wittaya Kanchanapusakit, Pattarapon Tanalikhit

Published Oct 23, 2023• 1 citation
arXivHTMLPDF

Abstract

We consider a heavy external object moving in an ideal gas of light particles. Collisions with the gas particles transfer momentum to the object, leading to a force that is proportional to the object's velocity but in the opposite direction. In an ideal classical gas at temperature T, the force acting on the object is proportional to T. Quantum statistics causes a deviation from the T-dependence and shows that the force scales with T2 at low temperatures. At T = 0, the force vanishes in a Bose gas but is finite in a Fermi gas.

DOI
10.1119/5.0127334

Related papers

Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas - eScholarship

Dirk-André Deckert, Jürg Martin Fröhlich, Peter Pickl +1 more

We study a system consisting of a heavy quantum particle, called tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density $\to\infty$). Our estimates allow us to interchange the thermodynamic with the mean-field limit.

•Sep 30, 2012•1 citation

Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

Dirk-André Deckert, Jürg Martin Fröhlich, Peter Pickl +1 more

We study a system consisting of a heavy quantum particle, called tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density $\to\infty$). Our estimates allow us to interchange the thermodynamic with the mean-field limit.

arXiv:1210.0253•Sep 30, 2012•1 citation

Effective Dynamics of a Heavy Particle in an Ideal Bose Gas in the Thermodynamic Limit

Dirk-André Deckert, Jürg Martin Fröhlich, Peter Pickl +1 more

We study a system of a heavy quantum particle, from now on called tracer particle, coupled to an ideal gas of $N$ light Bose particles with a ratio between the masses of the tracer particle and of a gas particle being proportional to the gas particle density. While all particles obey the non-relativistic dispersion relation, the tracer particle is also driven by an external potential and couples to the gas particles through a pair potential. We compare the corresponding quantum dynamics to effective dynamics, given by a Newtonian equation for the tracer particle and a corresponding effective equation for the Bose gas. We quantify the closeness of these two dynamics depending on the gas particle density and the volume of the support of their wave function. The provided estimates are such that we get convergence in any limit taking the density and the volume to infinity. In particular, they allow to interchange the thermodynamic with the mean field limit.

•Sep 30, 2012•0 citations

The Brownian Motion in an Ideal Quantum Qas

Chi-Chun Zhou, Zhang, Ping, Wu-Sheng Dai

A Brownian particle in an ideal quantum gas is considered. The mean square displacement (MSD) is derived. The Bose-Einstein or Fermi-Dirac distribution, other than the Maxwell-Boltzmann distribution, provides a different stochastic force compared with the classical Brownian motion. The MSD, which depends on the thermal wavelength and the density of medium particles, reflects the quantum effect on the Brownian particle explicitly. The result shows that the MSD in an ideal Bose gas is shorter than that in a Fermi gas. The behavior of the quantum Brownian particle recovers the classical Brownian particle as the temperature raises. At low temperatures, the quantum effect becomes obvious. For example, there is a random motion of the Brownian particle due to the fermionic exchange interaction even the temperature is near the absolute zero.

arXiv:2003.05288•Mar 9, 2020•0 citations

Quantum Statistics of Ideal Gases in Two Dimensions

Robert Mccredie May

It is shown that in two dimensions the specific heat ${C}_{V}(T, N)$ for an ideal gas of Fermi particles is identical with that for an ideal Bose gas for all $T$ and $N$. This is true despite the great difference in the distribution functions of the two systems at low temperatures. To shed further light on this identity, the quantum statistics of ideal gases are investigated treating the number of dimensions as a continuous variable: $n=2$ is seen to be a special case. In the extreme relativistic region, the analogous special case is $n=1$.

Physical Review•Sep 14, 1964•96 citations

Consequences of a Particle at X and a Force Acting Over dx and Quantum Mechanics

Francesco R. Ruggeri

Classical Newtonian mechanics separates a particle (effect) from a force (cause). A particle has properties at a given x (and time t), but if it interacts with a force, this interaction occurs over dt and dx. Given that many forces do not change in time, we argue that a notion of a force is inseparable from the idea of dx. If one gives the value of a force at x, this value acts within a dx, which in Newtonian mechanics tends to 0. We have argued before that a particle with momentum represents a force or impulse itself, but at the same time may receive impulse hits from other sources (e.g. a Newtonian force -dV/dx). If a particle represents a force(impulse) it should be inseparable from the notion of dx, even if it has a constant p (momentum) and is traveling through space. Thus the idea of a momentum defining an internal ruler gradation through a probability distribution in x which we have presented in previous notes is compatible with the idea of describing a particle as a force. If one only considers a particle as an effect, there would be no need to worry about dx until a force(x) appears. An internal dx is not defined by an external ruler and does not need to tend to 0 as in Newtonian mechanics. Rather it is statistical in nature as p is a fixed impulse, but the probability to be at different x points within dx (called a wavelength) differ. In (1) we compared a classical Maxwell-Boltzmann gas to a quantum free particle. We argued that d/d density Pressure = RT = average pressure of a particle. We suggested this is analogous to the quantum free particle situation: (-id/dx probability(p,x) ) / probability(p,x) = p where probability(p,x) is unnormalized. In other words a change in a probability yields a deterministic value p. The notion of a deterministic value p associated with a probability distribution in what would be another deterministic variable x in Newtonian mechanics (except now one has a dx distribution because the particle is a force/impulse) has consequences. If one wishes to have a particle sit at x=0, say in an oscillator system, one needs to use a wavelength which is fairly small and centered at x=0. The wavelength, however, is associated with momentum and even being small spreads out from x=0 meaning there is potential energy .5kxx as well. Thus one may use an ensemble of forces/impulses Sum over p a(p)exp(ipx) to create a “dx” about x=0, but at the same time this ensemble represents an average particle (defined at x with prms(x)) which must satisfy KE(x) + V(x) = En i.e. the classical conservation expression. In other words, one sees again that average statistical quantities may behave as deterministic ones.

•Apr 27, 2023•0 citations
We consider a heavy external object moving in an ideal gas of light particles. Collisions with the gas particles transfer momentum to the object, leading to a force that is proportional to the object's velocity but in the opposite direction. In an ideal classical gas at temperature T, the force acting on the object is proportional to T. Quantum statistics causes a deviation from the T-dependence and shows that the force scales with T2 at low temperatures. At T = 0, the force vanishes in a Bose gas but is finite in a Fermi gas.
We study a system consisting of a heavy quantum particle, called tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density →∞\to\infty→∞). Our estimates allow us to interchange the thermodynamic with the mean-field limit.
We study a system consisting of a heavy quantum particle, called tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density →∞\to\infty→∞). Our estimates allow us to interchange the thermodynamic with the mean-field limit.
We study a system of a heavy quantum particle, from now on called tracer particle, coupled to an ideal gas of NNN light Bose particles with a ratio between the masses of the tracer particle and of a gas particle being proportional to the gas particle density. While all particles obey the non-relativistic dispersion relation, the tracer particle is also driven by an external potential and couples to the gas particles through a pair potential. We compare the corresponding quantum dynamics to effective dynamics, given by a Newtonian equation for the tracer particle and a corresponding effective equation for the Bose gas. We quantify the closeness of these two dynamics depending on the gas particle density and the volume of the support of their wave function. The provided estimates are such that we get convergence in any limit taking the density and the volume to infinity. In particular, they allow to interchange the thermodynamic with the mean field limit.
A Brownian particle in an ideal quantum gas is considered. The mean square displacement (MSD) is derived. The Bose-Einstein or Fermi-Dirac distribution, other than the Maxwell-Boltzmann distribution, provides a different stochastic force compared with the classical Brownian motion. The MSD, which depends on the thermal wavelength and the density of medium particles, reflects the quantum effect on the Brownian particle explicitly. The result shows that the MSD in an ideal Bose gas is shorter than that in a Fermi gas. The behavior of the quantum Brownian particle recovers the classical Brownian particle as the temperature raises. At low temperatures, the quantum effect becomes obvious. For example, there is a random motion of the Brownian particle due to the fermionic exchange interaction even the temperature is near the absolute zero.
It is shown that in two dimensions the specific heat CV(T,N){C}_{V}(T, N)CV​(T,N) for an ideal gas of Fermi particles is identical with that for an ideal Bose gas for all TTT and NNN. This is true despite the great difference in the distribution functions of the two systems at low temperatures. To shed further light on this identity, the quantum statistics of ideal gases are investigated treating the number of dimensions as a continuous variable: n=2n=2n=2 is seen to be a special case. In the extreme relativistic region, the analogous special case is n=1n=1n=1.
Classical Newtonian mechanics separates a particle (effect) from a force (cause). A particle has properties at a given x (and time t), but if it interacts with a force, this interaction occurs over dt and dx. Given that many forces do not change in time, we argue that a notion of a force is inseparable from the idea of dx. If one gives the value of a force at x, this value acts within a dx, which in Newtonian mechanics tends to 0. We have argued before that a particle with momentum represents a force or impulse itself, but at the same time may receive impulse hits from other sources (e.g. a Newtonian force -dV/dx). If a particle represents a force(impulse) it should be inseparable from the notion of dx, even if it has a constant p (momentum) and is traveling through space. Thus the idea of a momentum defining an internal ruler gradation through a probability distribution in x which we have presented in previous notes is compatible with the idea of describing a particle as a force. If one only considers a particle as an effect, there would be no need to worry about dx until a force(x) appears. An internal dx is not defined by an external ruler and does not need to tend to 0 as in Newtonian mechanics. Rather it is statistical in nature as p is a fixed impulse, but the probability to be at different x points within dx (called a wavelength) differ. In (1) we compared a classical Maxwell-Boltzmann gas to a quantum free particle. We argued that d/d density Pressure = RT = average pressure of a particle. We suggested this is analogous to the quantum free particle situation: (-id/dx probability(p,x) ) / probability(p,x) = p where probability(p,x) is unnormalized. In other words a change in a probability yields a deterministic value p. The notion of a deterministic value p associated with a probability distribution in what would be another deterministic variable x in Newtonian mechanics (except now one has a dx distribution because the particle is a force/impulse) has consequences. If one wishes to have a particle sit at x=0, say in an oscillator system, one needs to use a wavelength which is fairly small and centered at x=0. The wavelength, however, is associated with momentum and even being small spreads out from x=0 meaning there is potential energy .5kxx as well. Thus one may use an ensemble of forces/impulses Sum over p a(p)exp(ipx) to create a “dx” about x=0, but at the same time this ensemble represents an average particle (defined at x with prms(x)) which must satisfy KE(x) + V(x) = En i.e. the classical conservation expression. In other words, one sees again that average statistical quantities may behave as deterministic ones.