We study an anisotropic variant of the
d-dimensional imperfect Bose gas, where the asymptotic behaviour of the dispersion
εk at vanishing momentum
k may differ from the standard quadratic form. The analysis reveals the key role of the shift exponent
ψ governing the asymptotic behaviour of the critical temperature
Tc(μ) as a function of the chemical potential
μ at
Tc→0. We argue that the universality classes of Bose-Einstein condensation admitted by the model may be classified according to the allowed values of
ψ so that spatial dimensionality has only an indirect impact on the transition properties. We analyse the correlation function of the model and discuss its asymptotics depending on the direction. Both for the perfect and imperfect anisotropic Bose gases, the correlation function
χ(x) at
T>Tc turns out to show either exponential decay or exponentially damped oscillatory behaviour depending on the orientation of
x with respect to the dispersion anisotropies.
We study an anisotropic variant of the
d-dimensional imperfect Bose gas on a lattice, where the asymptotic behavior of the dispersion
ϵk at vanishing momentum
k may differ from the standard quadratic form. We derive a general expression for the lower critical dimension
dL of the model and show that it may be pushed to arbitrarily high values by engineering the hopping parameters. The same applies to the upper critical dimension
dU. For
d>dL we find a general, exact expression for the Bose-Einstein condensation temperature
Tc(μ) as a function of the chemical potential
μ. The asymptotic behavior of
Tc(μ) at
Tc→0 is governed by the shift exponent
ψ, whose value turns out to fully determine whether the system is below or above the upper critical dimension. The critical exponents at condensation as well as the exponent
ψ may attain non-standard values for specific choices of the lattice kinetic couplings. Finally, we study the mechanism leading to the affinity between the imperfect Bose gas and the classical spherical model of spins in the critical regime.
Abstract We study an anisotropic variant of the d -dimensional imperfect Bose gas, where the asymptotic behaviour of the dispersion at vanishing momentum may differ from the standard quadratic form. The analysis reveals the key role of the shift exponent ψ governing the asymptotic behaviour of the critical temperature as a function of the chemical potential μ at . We argue that the universality classes of Bose–Einstein condensation admitted by the model may be classified according to the allowed values of ψ so that spatial dimensionality has only an indirect impact on the transition properties. We analyse the correlation function of the model and discuss its asymptotics depending on the direction. Both for the perfect and imperfect anisotropic Bose gases, the correlation function at turns out to show either exponential decay or exponentially damped oscillatory behaviour depending on the orientation of with respect to the dispersion anisotropies.
The dilute, two-dimensional Bose gas exhibits a novel regime of relaxational dynamics in the regime ${k}_{B}T\ensuremath{\gtrsim}\ensuremath{\mid}\ensuremath{\mu}\ensuremath{\mid}$ where
T is the absolute temperature and $\ensuremath{\mu}$ is the chemical potential. This may also be interpreted as the quantum criticality of the zero density quantum critical point at $\ensuremath{\mu}=0$. We present a theory for this dynamic, to leading order in $1∕\mathrm{ln}[\ensuremath{\Lambda}∕({k}_{B}T)]$, where $\ensuremath{\Lambda}$ is a high energy cutoff. Although pairwise interactions between the bosons are weak at low energy scales, the collective dynamics are strongly coupled even when $\mathrm{ln}(\ensuremath{\Lambda}∕T)$ is large. We argue that the strong-coupling effects can be isolated in an effective classical model, which is then solved numerically. Applications to experiments on the gap-closing transition of spin-gap antiferromagnets in an applied field are presented.
Ideal Bose-Einstein condensation (BEC) remains a paradigmatic example of a continuous phase transition and a cornerstone for understanding quantum degenerate bosonic matter. We demonstrate that critical behavior of the ideal Bose gas near the BEC phase transition falls into three distinct classes, determined exclusively by the low-energy scaling of the density of states. Depending on its scaling exponent, which is controlled by dimensionality and confinement, the transition displays either the usual algebraic divergences of thermodynamic susceptibilities, divergent behavior with marginal logarithmic corrections, or a more subtle form of criticality, where only the correlation length diverges. Our work provides a unified framework for criticality in noninteracting bosonic systems. This classification applies broadly to atomic, photonic, polaritonic, and magnonic condensates, where dimensionality, confinement, and spectral engineering can strongly reshape the density of states.
We study the quantum phase transition in an atomic Bose gas near a Feshbach resonance in terms of the renormalization group. This quantum phase transition is characterized by an Ising order parameter. We show that in the low temperature regime where the quantum fluctuations dominate the low-energy physics this phase transition is of first order because of the coupling between the Ising order parameter and the Goldstone mode existing in the bosonic superfluid. However, when the thermal fluctuations become important, the phase transition turns into the second order one, which belongs to the three-dimensional Ising universality class. We also calculate the damping rate of the collective mode in the phase with only a molecular Bose-Einstein condensate near the second-order transition line, which can serve as an experimental signature of the second-order transition.