A finite temperature field theory of the lambda transition

Peter Arnold, Boris Tom, Á Sik

I review the Bose-Einstein condensation phase transition of dilute gases of cold atoms, for particle theorists acquainted with methods of field theory at finite temperature. I then discuss how the dependence of the phase transition temperature on the interaction strength can be computed in the large N approximation. 1 Phase Transitions in Hot Scalar Theories The standard example from particle physics of a scalar theory is the Higgs sector of electroweak theory, which has a phase transition (or a crossover) at a temperature of order the weak scale: say, a few hundred GeV or so. Let’s focus on pure scalar theory by imagining setting the gauge coupling constant gw to zero. At finite temperature, the Higgs picks up a thermal contribution #λT 2 to its effective mass, and the effective potential becomes roughly of the form V (φ) ∼ m 2 eff (T)φ2 + λφ 4 with m 2 eff (T) = −M2 + #λT 2. At sufficiently high temperature, the #λT 2 turns the potential from being concave down at the origin to concave up, and so restores the symmetry that is spontaneously broken at zero temperature.

Tadashi Toyoda

V. Dohm

Kris T. Delaney, Henri Orland, Glenn H. Fredrickson

We report a stable and efficient complex Langevin sampling scheme for performing approximation-free numerical simulations directly on the path-integral coherent-states field theory for an assembly of interacting bosons. We apply the method to generate the λ line of critical phase transitions associated with Bose-Einstein condensation in a model ϕ^{4} scalar field theory. The new approach enjoys near-linear scaling in the resolved (d+1) spatial and imaginary-time dimensions and should be particularly efficient for the study of dense systems at low temperature.

M. A. van Eijck

T. Matos, Abril Suárez

Starting with a scalar field in a thermal bath and using the one-loop quantum correction potential, we rewrite the Klein-Gordon equation in its thermodynamical representation and study the behavior of this scalar field due to temperature variations in the equations of motion. We find the generalization of a Gross-Pitaevskii–like equation for a relativistic Bose gas with finite temperature, the corresponding thermodynamic and viscosity expressions, and an expression for the postulate of the first law of the thermodynamics for this BECs. We also propose that the equations obtained might help to explain at some level the phase transition of a Bose-Einstein Condensate in terms of quantum field theory in a simple way.