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Register a new userThermodynamic instability and first-order phase transition in an ideal Bose gas
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We conduct a rigorous investigation into the thermodynamic instability of ideal Bose gas confined in a cubic box, without assuming thermodynamic limit nor continuous approximation. Based on the exact expression of canonical partition function, we perform numerical computations up to the number of particles one million. We report that if the number of particles is equal to or greater than a certain critical value, which turns out to be 7616, the ideal Bose gas subject to Dirichlet boundary condition reveals a thermodynamic instability. Accordingly we demonstrate - for the first time - that, a system consisting of finite number of particles can exhibit a discontinuous phase transition featuring a genuine mathematical singularity, provided we keep not volume but pressure constant. The specific number, 7616 can be regarded as a characteristic number of cube that is the geometric shape of the box.
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In current experiments with cold quantum gases in periodic potentials, interference fringe contrast is typically the easiest signal in which to look for effects of non-trivial many-body dynamics. In order better to calibrate such measurements, we analyse the background effect of thermal decoherence as it occurs in the absence of dynamical interparticle interactions. We study the effect of optical lattice potentials, as experimentally applied, on the condensed fraction of a non-interacting Bose gas in local thermal equilibrium at finite temperatures. We show that the experimentally observed decrease of the condensate fraction in the presence of the lattice can be attributed, up to a threshold lattice height, purely to ideal gas thermodynamics; conversely we confirm that sharper decreases in first-order coherence observed in stronger lattices are indeed attributable to many-body physics. Our results also suggest that the fringe visibility kinks observed in F.Gerbier et al., Phys. Rev. Lett. 95, 050404 (2005) may be explained in terms of the competition between increasing lattice strength and increasing mean gas density, as the gaussian profile of the red-detuned lattice lasers also increases the effective strength of the harmonic trap.
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We present a microscopic theory of the second order phase transition in an interacting Bose gas that allows one to describe formation of an ordered condensate phase from a disordered phase across an entire critical region continuously. We derive the exact fundamental equations for a condensate wave function and the Green functions, which are valid both inside and outside the critical region. They are reduced to the usual Gross-Pitaevskii and Beliaev-Popov equations in a low-temperature limit outside the critical region. The theory is readily extendable to other phase transitions, in particular, in the physics of condensed matter and quantum fields.
Dark states are stationary states of a dissipative, Lindblad-type time evolution with zero von Neumann entropy, therefore representing examples of pure, steady quantum states. Non-equilibrium dynamics featuring a dark state recently gained a lot of attraction since their implementation in the context of driven-open quantum systems represents a viable possibility to engineer unique, pure states. In this work, we analyze a driven many-body spin system, which undergoes a transition from a dark steady state to a mixed steady state as a function of the driving strength. This transition connects a zero entropy (dark) state with a finite entropy (mixed) state and thus goes beyond the realm of equilibrium statistical mechanics and becomes of genuine nonequilibrium character. We analyze the relevant long wavelength fluctuations driving this transition in a regime where the system performs a discontinuous jump from a dark to a mixed state by means of the renormalization group. This allows us to approach the nonequilibrium dark state transition and identify similarities and clear differences to common, equilibrium phase transitions, and to establish the phenomenology for a first order dark state phase transition.
We consider an ideal Bose gas contained in a cylinder in three spatial dimensions, subjected to a uniform gravitational field. It has been claimed by some authors that there is discrepancy between the semi-classical and quantum calculations in the thermal properties of such a system. To check this claim, we calculate the heat capacity and isothermal compressibility of this system semi-classically as well as from the quantum spectrum of the density of states. The quantum calculation is done for a finite number of particles. We find good agreement between the two calculations when the number of particles are taken to be large. We also find that this system has the same thermal properties as an ideal five dimensional Bose gas.
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