Interference of identical particles and the quantum work distribution

Quantum-mechanical particles in a confining potential interfere with each other while undergoing thermodynamic processes far from thermal equilibrium. By evaluating the corresponding transition probabilities between many-particle eigenstates we obtain the quantum work distribution function for identical bosons and fermions, which we compare with the case of distinguishable particles. We find that the quantum work distributions for bosons and fermions significantly differ at low temperatures, while, as expected, at high temperatures the work distributions converge to the classical expression. These findings are illustrated with two analytically solvable examples, namely the time-dependent infinite square well and the parametric harmonic oscillator.

Figure 1

Cumulative work distribution (13) for two bosons (blue dotted line), fermions (black dashed line), and distinguishable particles (red solid line) in an expanding piston with ${\lambda }_0=1,{\lambda }_{\tau }=2$, and $v=0.1$. Temperatures are, from top to bottom, ${\beta }^{-1}=0,{\beta }^{-1}=10,{\beta }^{-1}=20$, and ${\beta }^{-1}=100$.

Figure 2

Cumulative work distribution (13) for two bosons (blue dotted line), fermions (black dashed line), and distinguishable particles (red solid line) in an expanding piston with ${\lambda }_0=1,{\lambda }_{\tau }=2$, and $v=8$. Temperatures are, from top to bottom, ${\beta }^{-1}=0,{\beta }^{-1}=10,{\beta }^{-1}=20$, and ${\beta }^{-1}=100$.

Figure 3

Cumulative work distribution (13) for two bosons (blue dotted line), fermions (black dashed line), and distinguishable particles (red solid line) in an expanding piston with ${\lambda }_0=1,{\lambda }_{\tau }=2$, and $v=100$. Temperatures are, from top to bottom, ${\beta }^{-1}=0,{\beta }^{-1}=10,{\beta }^{-1}=20$, and ${\beta }^{-1}=100$.

Figure 4

Cumulative work distribution (13) for three bosons (blue dotted line), fermions (black dashed line), and distinguishable particles (red solid line) in an expanding piston with ${\lambda }_0=1,{\lambda }_{\tau }=2$, and $v=8$. Temperatures are, from top to bottom, ${\beta }^{-1}=0,{\beta }^{-1}=10$, and ${\beta }^{-1}=20$.

Figure 5

Cumulative work distribution (13) for three bosons (blue dotted line), fermions (black dashed line), and distinguishable particles (red solid line) in an expanding piston with ${\lambda }_0=1,{\lambda }_{\tau }=2$, and $v=100$. Temperatures are, from top to bottom, ${\beta }^{-1}=0$ and ${\beta }^{-1}=10$.

Figure 6

Cumulative work distribution (13) for two bosons (blue dotted line), fermions (black dashed line), and distinguishable particles (red solid line) in a quenched harmonic potential (14) with ${\omega }_0=1,{\omega }_{\tau }=\sqrt{2}$, and $1/\tau =0.1$. Temperatures are, from top to bottom, ${\beta }^{-1}=0,{\beta }^{-1}=0.5,{\beta }^{-1}=1$, and ${\beta }^{-1}=5$.

Figure 7

Cumulative work distribution (13) for two bosons (blue dotted line), fermions (black dashed line), and distinguishable particles (red solid line) in a quenched harmonic potential (14) with ${\omega }_0=1,{\omega }_{\tau }=\sqrt{2}$, and $1/\tau =100$. Temperatures are, from top to bottom, ${\beta }^{-1}=0,{\beta }^{-1}=0.5$, and ${\beta }^{-1}=1$.

Figure 8

Cumulative work distribution (13) for three bosons (blue dotted line), fermions (black dashed line), and distinguishable particles (red solid line) in a quenched harmonic potential (14) with ${\omega }_0=1,{\omega }_{\tau }=\sqrt{2}$, and $1/\tau =0.1$. Temperatures are, from top to bottom, ${\beta }^{-1}=0$ and ${\beta }^{-1}=0.5$.

Figure 9

Cumulative work distribution (13) for three bosons (blue dotted line), fermions (black dashed line), and distinguishable particles (red solid line) in a quenched harmonic potential (14) with ${\omega }_0=1,{\omega }_{\tau }=\sqrt{2}$, and $1/\tau =100$. Temperatures are, from top to bottom, ${\beta }^{-1}=0$ and ${\beta }^{-1}=0.5$.