The Influence of the Symmetry of Identical Particles on Flight Times

In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ-barrier. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two sets of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a `screen’ is calculated in each case from the density and flux. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down the propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain, and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier and later than bosons when they are scattered by a δ-barrier. Although the particle symmetry does affect the mean tunneling flight time, in the limit of narrow in momentum initial Gaussian wave functions, the mean times are not affected by symmetry but tend to the phase time for distinguishable particles.

Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field

We derive the general exact forms of the Wigner function, of mean values of conserved currents, of the spin density matrix, of the spin polarization vector and of the distribution function of massless particles for the free Dirac field at global thermodynamic equilibrium with rotation and acceleration, extending our previous results obtained for the scalar field. The solutions are obtained by means of an iterative method and analytic continuation, which lead to formal series in thermal vorticity. In order to obtain finite values, we extend to the fermionic case the method of analytic distillation introduced for bosonic series. The obtained mean values of the stress-energy tensor, vector and axial currents for the massless Dirac field are in agreement with known analytic results in the special cases of pure acceleration and pure rotation. By using this approach, we obtain new expressions of the currents for the more general case of combined rotation and acceleration and, in the pure acceleration case, we demonstrate that they must vanish at the Unruh temperature.

The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical

For a harmonically trapped system consisting of two bosons in one spatial dimension with infinite contact repulsion (hard core bosons), we derive an expression for the one-body density matrix $$\rho _\mathrm{B}$$ ρ B in terms of center of mass and relative coordinates of the particles. The deviation from $$\rho _\mathrm{F}$$ ρ F , the density matrix for the two fermions case, can be clearly identified. Moreover, the obtained $$\rho _\mathrm{B}$$ ρ B allows us to derive a closed form expression of the corresponding momentum distribution $$n_\mathrm{B}(p)$$ n B ( p ) . We show how the result deviates from the noninteracting fermionic case, the deviation being associated with the short-range character of the interaction. Mathematically, our analytical momentum distribution is expressed in terms of one and two variables confluent hypergeometric functions. Our formula satisfies the correct normalization and possesses the expected behavior at zero momentum. It also exhibits the high momentum $$1/p^4 $$ 1 / p 4 tail with the appropriate Tan’s coefficient. Numerical results support our findings.

Reflected entropy for free scalars

We continue our study of reflected entropy, R(A, B), for Gaussian systems. In this paper we provide general formulas valid for free scalar fields in arbitrary dimensions. Similarly to the fermionic case, the resulting expressions are fully determined in terms of correlators of the fields, making them amenable to lattice calculations. We apply this to the case of a (1 + 1)-dimensional chiral scalar, whose reflected entropy we compute for two intervals as a function of the cross-ratio, comparing it with previous holographic and free-fermion results. For both types of free theories we find that reflected entropy satisfies the conjectural monotonicity property R(A, BC) ≥ R(A, B). Then, we move to (2 + 1) dimensions and evaluate it for square regions for free scalars, fermions and holography, determining the very-far and very-close regimes and comparing them with their mutual information counterparts. In all cases considered, both for (1 + 1)- and (2 + 1)-dimensional theories, we verify that the general inequality relating both quantities, R(A, B) ≥ I (A, B), is satisfied. Our results suggest that for general regions characterized by length-scales LA ∼ LB ∼ L and separated a distance ℓ, the reflected entropy in the large-separation regime (x ≡ L/ℓ ≪ 1) behaves as R(x) ∼ −I(x) log x for general CFTs in arbitrary dimensions.

Parafermion theory from the q-deformed algebra with q a root of unity

In this paper, we find the [Formula: see text]-deformed algebra with the finite- and infinite-dimensional Fock space and both the fermionic limit and the bosonic limit. Using the cardinality of set theory, we propose the Hamiltonian interpolating bosonic case and fermionic case, which enables us to construct the proper partition function and internal energy. As examples, we discuss the specific heat of free [Formula: see text] parafermion gas model and [Formula: see text] parafermion star.

Two component boson–fermion plasma at finite temperature

We discuss thermodynamic stability of neutral real (quantum) matter from the point of view of a computer experiment at finite, nonzero, temperature. We perform (restricted) path integral Monte Carlo simulations of the two component plasma where the two species are both bosons, both fermions, and one boson and one fermion. We calculate the structure of the plasma and discuss about the formation of binded couples of oppositely charged particles. The purely bosonic case is thermodynamically unstable. In this case we find an undetermined size-dependent contact value unlike partial radial distribution function. For the purely fermionic case, we find a demixing transition with binding also of like species.

Qubit Dynamics in a q-Deformed Oscillators Environment

We study the dynamics of one and two qubits plunged in a q-deformed oscillators environment. Specifically we evaluate the decay of quantum coherence and entanglement in time when passing from bosonic to fermionic environments. Slowing down of decoherence in the fermionic case is found. The effect manifests itself only at finite temperature.

DYNAMIC PAIR EXCITATIONS IN ALUMINUM

We present a calculation of the excitation spectrum of the electron liquid that includes time-dependent pair correlations. For the charged boson fluid these correlations provide a major mechanism for lowering the plasmon energy; here we extend that study to the much more demanding fermionic case. Based on the formalism of correlated basis functions we derive coupled equations of motion for time-dependent 1- and 2-particle correlation amplitudes. Our solution strategy for these equations ensures the fulfillment of the first two energy–weighted sum rules and, in the appropriate limit, is consistent with the bosonic version. Results are presented for the dynamic structure factor with special emphasis being put on studying the double plasmon.