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John F. Dawson

Publications and source records attributed to John F. Dawson.

At least 37 records · Page 2Linked to original sources
arXiv2013

Leading-Order Auxiliary Field Theory of the Bose-Hubbard Model

We discuss the phase diagram of the Bose-Hubbard (BH) model in the leading-order auxiliary field (LOAF) theory. LOAF is a conserving non-perturbative approximation that treats on equal footing the normal and anomalous density condensates. The mean-field solutions in LOAF correspond to first-order and second-order phase transition solutions with two critical temperatures corresponding to a vanishing Bose-Einstein condensate, $T_c$, and a vanishing diatom condensate, $T^\star$. The \emph{second-order} phase transition solution predicts the correct order of the transition in continuum Bose gases. For either solution, the superfluid state is tied to the presence of the diatom condensate related to the anomalous density in the system. In ultracold Bose atomic gases confined on a three-dimensional lattice, the critical temperature $T_c$ exhibits a quantum phase transition, where $T_c$ goes to zero at a finite coupling. The BH phase diagram in LOAF features a line of first-order transitions ending in a critical point beyond which the transition is second order while approaching the quantum phase transition. We identify a region where a diatom condensate is expected for temperatures higher than $T_c$ and less than $T_0$, the critical temperature of the non-interacting system. The LOAF phase diagram for the BH model compares qualitatively well with existing experimental data and results of \emph{ab initio} Monte Carlo simulations.

cond-mat.quant-gas↗
arXiv2012

Composite-Field Goldstone States and Higgs Mechanism in Dilute Bose Gases

We show that a composite-field (diatom) Goldstone state is expected in a dilute Bose gas for temperatures between the Bose gas critical temperature where the atom Bose-Einstein condensate appears and the temperature where superfluidity sets in. The presence of superfluidity is tied to the existence of a U(1) charge-two diatom condensate in the system. By promoting the global U(1) symmetry of the theory to a gauge symmetry, we find that the mass of the gauge particle generated through the Anderson-Higgs mechanism is related to the superfluid density via the Meissner effect and the superfluid density is related to the square of the anomalous density in the Bose system.

cond-mat.quant-gas↗
arXiv2011

The Josephson relation for the superfluid density and the connection to the Goldstone theorem in dilute Bose atomic gasses

We derive the Josephson relation for a dilute Bose gas in the framework of an auxiliary-field resummation of the theory in terms of the normal- and anomalous-density condensates. The mean-field phase diagram of this theory features two critical temperatures, T_c and $T^*, associated with the presence in the system of the Bose-Einstein condensate (BEC) and superfluid state, respectively. In this context, the Josephson relation shows that the superfluid density is related to a second order parameter, the square of the anomalous-density condensate. This is in contrast with the corresponding result in the Bose gas theory without an anomalous condensate, which predicts that the superfluid density is proportional to the BEC condensate density. Our findings are consistent with the prediction that in the temperature range between T_c and T^* a fraction of the system is in the superfluid state in the absence of the BEC condensate. This situation is similar to the case of dilute Fermi gases, where the superfluid density is proportional to the square of the gap parameter. The Josephson relation relies on the existence of zero energy and momentum excitations showing the intimate relationship between superfluidity and the Goldstone theorem.

cond-mat.quant-gas↗
arXiv2011

Analytical limits for cold atom Bose gases with tunable interactions

We discuss the equilibrium properties of dilute Bose gases using a non-perturbative formalism based on auxiliary fields related to the normal and anomalous densities. We show analytically that for a dilute Bose gas of weakly-interacting particles at zero temperature, the leading-order auxiliary field (LOAF) approximation leads to well-known analytical results. Close to the critical point the LOAF predictions are the same as those obtained using an effective field theory in the large-N approximation. We also report analytical approximations for the LOAF results in the unitarity limit, which compare favorably with our numerical results. LOAF predicts that the equation of state for the Bose gas in the unitarity limit is E / (p V) = 1, unlike the case of the Fermi gas when E / (p V) = 3/2.

cond-mat.quant-gas↗
arXiv2011

Auxiliary field approach to dilute Bose gases with tunable interactions

We rewrite the Lagrangian for a dilute Bose gas in terms of auxiliary fields related to the normal and anomalous condensate densities. We derive the loop expansion of the effective action in the composite-field propagators. The lowest-order auxiliary field (LOAF) theory is a conserving mean-field approximation consistent with the Goldstone theorem without some of the difficulties plaguing approximations such as the Hartree and Popov approximations. LOAF predicts a second-order phase transition. We give a set of Feynman rules for improving results to any order in the loop expansion in terms of composite-field propagators. We compare results of the LOAF approximation with those derived using the Popov approximation. LOAF allows us to explore the critical regime for all values of the coupling constant and we determine various parameters in the unitarity limit.

cond-mat.quant-gas↗
arXiv2011

Auxiliary field formalism for dilute fermionic atom gases with tunable interactions

We develop the auxiliary field formalism corresponding to a dilute system of spin-1/2 fermions. This theory represents the Fermi counterpart of the BEC theory developed recently by F. Cooper et al. [Phys. Rev. Lett. 105, 240402 (2010)] to describe a dilute gas of Bose particles. Assuming tunable interactions, this formalism is appropriate for the study of the crossover from the regime of Bardeen-Cooper-Schriffer (BCS) pairing to the regime of Bose-Einstein condensation (BEC) in ultracold fermionic atom gases. We show that when applied to the Fermi case at zero temperature, the leading-order auxiliary field (LOAF) approximation gives the same equations as those obtained in the standard BCS variational picture. At finite temperature, LOAF leads to the theory discussed by by Sa de Melo, Randeria, and Engelbrecht [Phys. Rev. Lett. 71, 3202(1993); Phys. Rev. B 55, 15153(1997)]. As such, LOAF provides a unified framework to study the interacting Fermi gas. The mean-field results discussed here can be systematically improved upon by calculating the one-particle irreducible (1-PI) action corrections, order by order.

cond-mat.quant-gas↗
arXiv2010

Non-perturbative predictions for cold atom Bose gases with tunable interactions

We derive a theoretical description for dilute Bose gases as a loop expansion in terms of composite-field propagators by rewriting the Lagrangian in terms of auxiliary fields related to the normal and anomalous densities. We demonstrate that already in leading order this non-perturbative approach describes a large interval of coupling-constant values, satisfies Goldstone's theorem, yields a Bose-Einstein transition that is second-order, and is consistent with the critical temperature predicted in the weak-coupling limit by the next-to-leading order large-N expansion.

cond-mat.quant-gas↗
arXiv2009

Fermion particle production in semi-classical Boltzmann-Vlasov transport theory

We present numerical solutions of the semi-classical Boltzmann-Vlasov equation for fermion particle-antiparticle production by strong electric fields in boost-invariant coordinates in (1+1) and (3+1) dimensional QED. We compare the Boltzmann-Vlasov results with those of recent quantum field theory calculations and find good agreement. We conclude that extending the Boltzmann-Vlasov approach to the case of QCD should allow us to do a thorough investigation of how back-reaction affects recent results on the dependence of the transverse momentum distribution of quarks and anti-quarks on a second Casimir invariant of color SU(3).

hep-ph↗
arXiv2009

Backreaction and Particle Production in (3+1)-dimensional QED

We study the fermion pair production from a strong electric field in boost-invariant coordinates in (3+1) dimensions and exploit the cylindrical symmetry of the problem. This problem has been used previously as a toy model for populating the central-rapidity region of a heavy-ion collision (when we can replace the electric by a chromoelectric field). We derive and solve the renormalized equations for the dynamics of the mean electric field and current of the produced particles, when the field is taken to be a function only of the fluid proper time $τ= \sqrt{t^2-z^2}$. We determine the proper-time evolution of the comoving energy density and pressure of the ensuing plasma and the time evolution of suitable interpolating number operators. We find that unlike in (1+1) dimensions, the energy density closely follows the longitudinal pressure. The transverse momentum distribution of fermion pairs at large momentum is quite different and larger than that expected from the constant field result.

hep-ph↗
arXiv2009

On the forward cone quantization of the Dirac field in "longitudinal boost-invariant" coordinates with cylindrical symmetry

We obtain a complete set of free-field solutions of the Dirac equation in a (longitudinal) boost-invariant geometry with azimuthal symmetry and use these solutions to perform the canonical quantization of a free Dirac field of mass $M$. This coordinate system which uses the 1+1 dimensional fluid rapidity $η= 1/2 \ln [(t-z)/(t+z)]$ and the fluid proper time $τ= (t^2-z^2)^{1/2}$ is relevant for understanding particle production of quarks and antiquarks following an ultrarelativistic collision of heavy ions, as it incorporates the (approximate) longitudinal "boost invariance" of the distribution of outgoing particles. We compare two approaches to solving the Dirac equation in curvilinear coordinates, one directly using Vierbeins, and one using a "diagonal" Vierbein representation.

hep-ph↗
arXiv2008

Casimir dependence of transverse distribution of pairs produced from a strong constant chromo-electric background field

The transverse distribution of gluon and quark-antiquark pairs produced from a strong constant chromo-electric field depends on two gauge invariant quantities, $C_1=E^aE^a$ and $C_2=[d_{abc}E^aE^bE^c]^2$, as shown earlier in [G.C. Nayak and P. van Nieuwenhuizen, Phys. Rev. D 71, 125001 (2005)] for gluons and in [G.C. Nayak, Phys. Rev. D 72, 125010 (2005)] for quarks. Here, we discuss the explicit dependence of the distribution on the second Casimir invariant, C_2, and show the dependence is at most a 15% effect.

hep-ph↗
arXiv2008

Fermion pair production in QED and the backreaction problem in (1+1)-dimensional boost-invariant coordinates revisited

We study two different initial conditions for fermions for the problem of pair production of fermions coupled to a classical electromagnetic field with backreaction in \oneplusone boost-invariant coordinates. Both of these conditions are consistent with fermions initially in a vacuum state. We present results for the proper time evolution of the electric field $E$, the current, the matter energy density, and the pressure as a function of the proper time for these two cases. We also determine the interpolating number density as a function of the proper time. We find that when we use a "first order adiabatic" vacuum initial condition or a "free field" initial condition for the fermion field, we obtain essentially similar behavior for physically measurable quantities. The second method is computationally simpler, it is twice as fast and involves half the storage required by the first method.

hep-ph↗
arXiv2005

Supersymmetric approximations to the 3D supersymmetric O(N) model

We develop several non-perturbative approximations for studying the dynamics of a supersymmetric O(N) model which preserve supersymmetry. We study the phase structure of the vacuum in both the leading order in large-N approximation as well as in the Hartree approximation, and derive the finite temperature renormalized effective potential. We derive the exact Schwinger-Dyson equations for the superfield Green functions and develop the machinery for going beyond the next to leading order in large-N approximation using a truncation of these equations which can also be derived from a two-particle irreducible effective action.

hep-ph↗
arXiv2005

Renormalized broken-symmetry Schwinger-Dyson equations and the 2PI-1/N expansion for the O(N) model

We derive the renormalized Schwinger-Dyson equations for the one- and two-point functions in the auxiliary field formulation of $λϕ^4$ field theory to order 1/N in the 2PI-1/N expansion. We show that the renormalization of the broken-symmetry theory depends only on the counter terms of the symmetric theory with $ϕ= 0$. We find that the 2PI-1/N expansion violates the Goldstone theorem at order 1/N. In using the O(4) model as a low energy effective field theory of pions to study the time evolution of disoriented chiral condensates one has to {\em{explicitly}} break the O(4) symmetry to give the physical pions a nonzero mass. In this effective theory the {\em additional} small contribution to the pion mass due to the violation of the Goldstone theorem in the 2-PI-1/N equations should be numerically unimportant.

hep-ph↗
arXiv2004

Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of $λϕ^4$ field theory

In this paper we study the renormalization of the Schwinger-Dyson equations that arise in the auxiliary field formulation of the O(N) $ϕ^4$ field theory. The auxiliary field formulation allows a simple interpretation of the large-N expansion as a loop expansion of the generating functional in the auxiliary field $χ$, once the effective action is obtained by integrating over the $ϕ$ fields. Our all orders result is then used to obtain finite renormalized Schwinger-Dyson equations based on truncation expansions which utilize the two-particle irreducible (2-PI) generating function formalism. We first do an all orders renormalization of the two- and three-point function equations in the vacuum sector. This result is then used to obtain explicitly finite and renormalization constant independent self-consistent S-D equations valid to order~1/N, in both 2+1 and 3+1 dimensions. We compare the results for the real and imaginary parts of the renormalized Green's functions with the related \emph{sunset} approximation to the 2-PI equations discussed by Van Hees and Knoll, and comment on the importance of the Landau pole effect.

hep-ph↗
arXiv2002

Quantum dynamics of phase transitions in broken symmetry $λϕ^4$ field theory

We perform a detailed numerical investigation of the dynamics of broken symmetry $λϕ^4$ field theory in 1+1 dimensions using a Schwinger-Dyson equation truncation scheme based on ignoring vertex corrections. In an earlier paper, we called this the bare vertex approximation (BVA). We assume the initial state is described by a Gaussian density matrix peaked around some non-zero value of $<ϕ(0)>$, and characterized by a single particle Bose-Einstein distribution function at a given temperature. We compute the evolution of the system using three different approximations: Hartree, BVA and a related 2PI-1/N expansion, as a function of coupling strength and initial temperature. In the Hartree approximation, the static phase diagram shows that there is a first order phase transition for this system. As we change the initial starting temperature of the system, we find that the BVA relaxes to a new final temperature and exhibits a second order phase transition. We find that the average fields thermalize for arbitrary initial conditions in the BVA, unlike the behavior exhibited by the Hartree approximation, and we illustrate how $<ϕ(t)>$ and $<χ(t)>$ depend on the initial temperature and on the coupling constant. We find that the 2PI-1/N expansion gives dramatically different results for $<ϕ(t)>$.

hep-ph↗