Dimensional crossover of a boson gas in multilayers

Abstract

We obtain the thermodynamic properties for a non-interacting Bose gas constrained on multilayers modeled by a periodic Kronig-Penney delta potential in one direction and allowed to be free in the other two directions. We report Bose-Einstein condensation (BEC) critical temperatures, chemical potential, internal energy, specific heat, and entropy for different values of a dimensionless impenetrability $P⩾0$ between layers. The BEC critical temperature $T_c$ coincides with the ideal gas BEC critical temperature $T_0$ when $P=0$ and rapidly goes to zero as $P$ increases to infinity for any finite interlayer separation. The specific heat $C_V$ \textit{vs} $T$ for finite $P$ and plane separation $a$ exhibits one minimum and one or two maxima in addition to the BEC, for temperatures larger than $T_c$ which highlights the effects due to particle confinement. Then we discuss a distinctive dimensional crossover of the system through the specific heat behavior driven by the magnitude of $P$. For $T<T_c$ the crossover is revealed by the change in the slope of $\log C_V(T)$ and when $T>T_c$, it is evidenced by a broad minimum in $C_V(T)$.

Ten pages, nine figures

References in corpus (9)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms
• Finite temperature theory of superfluid bosons in optical lattices
• Thin helium film on a glass substrate
• Critical temperature of a Bose gas in an optical lattice
• Studies of bosons in optical lattices in a harmonic potential
• Finite temperature coherence of the ideal Bose gas in an optical lattice
• Bose-Einstein condensation in multilayers

Cited by in corpus (6)

• Specific heat of underdoped cuprate superconductors from a phenomenological layered Boson-Fermion model
• Trapping effect of periodic structures on the thermodynamic properties of Fermi and Bose gases
• Boson gas in a periodic array of tubes
• Bose gas in disordered, finite-layered systems
• Universal behavior of the BEC critical temperature for a multislab ideal Bose gas
• BEC and dimensional crossover in a boson gas within multi-slabs