Three-dimensional Quantum Slit Diffraction and Diffraction in Time

We study the quantum slit diffraction problem in three dimensions. In the treatment of diffraction of particles by a slit, it is usually assumed that the motion perpendicular to the slit is classical. Here we take into account the effect of the quantum nature of the motion perpendicular to the slit using the Green function approach [18]. We treat the diffraction of a Gaussian wave packet for general boundary conditions on the shutter. The difference between the standard and our three-dimensional slit diffraction models is analogous to the diffraction in time phenomenon introduced in [16]. We derive corrections to the standard formula for the diffraction pattern, and we point out situations in which this might be observable. In particular, we discuss the diffraction in space and time in the presence of gravity

The second critical point for the Perfect Bose gas in quasi-one-dimensional traps

We present a new model of quasi-one-dimensional trap with some unknown physical predictions about a second transition, including about a change in fractions of condensed coherence lengths due to the existence of a second critical temperature Tm < Tc. If this physical model is acceptable, we want to challenge experimental physicists in this regard

Discrete-Time Path Distributions on Hilbert Space

We construct a path distribution representing the kinetic part of the Feynman path integral at discrete times similar to that defined by Thomas [1], but on a Hilbert space of paths rather than a nuclear sequence space. We also consider different boundary conditions and show that the discrete-time Feynman path integral is well-defined for suitably smooth potentials

Nonadiabatic energy fluctuations of scale-invariant quantum systems in a time-dependent trap

We consider the nonadiabatic energy fluctuations of a many-body system in a time-dependent harmonic trap. In the presence of scale-invariance, the dynamics becomes self-similar and the nondiabatic energy fluctuations can be found in terms of the initial expectation values of the second moments of the Hamiltonian, square position, and squeezing operators. Nonadiabatic features are expressed in terms of the scaling factor governing the size of the atomic cloud, which can be extracted from time-of-flight images. We apply this exact relation to a number of examples: the single-particle harmonic oscillator, the one-dimensional Calogero-Sutherland model, describing bosons with inverse-square interactions that includes the non-interacting Bose gas and the Tonks-Girdardeau gas as limiting cases, and the unitary Fermi gas. We illustrate these results for various expansion protocols involving sudden quenches of the trap frequency, linear ramps and shortcuts to adiabaticity. Our results pave the way to the experimental study of nonadiabatic energy fluctuations in driven quantum fluids.Comment: 13 pages, 3 figures, minor change

Feynman Path Integral approach to electron diffraction for one and two slits, analytical results

In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we exhibit various approximations of the electron distribution which facilitate the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could therefore also serve as an interesting pedagogical introduction to Feynman's formulation of quantum mechanics for university students dealing with the foundations of quantum mechanics