Testing nucleation theory in two dimensions

We calculate bubble-nucleation rates for (2+1)-dimensional scalar theories at high temperature. Our approach is based on the notion of a real coarse-grained potential. The region of applicability of our method is determined through internal consistency criteria. We compare our results with data from lattice simulations. Good agreement is observed when the renormalized action of the simulated theory is known.     

Lattice topological field theory in two dimensions

The lattice definition of a two-dimensional topological field theory (TFT) is given generically, and the exact solution is obtained explicitly. In particular, the set of all lattice topological field theories is shown to be in one-to-one correspondence with the set of all associative algebrasR, and the physical Hilbert space is identified with the centerZ(R) of the associative algebraR. Perturbations of TFT's are also considered in this approach, showing that the form of topological perturbations is automatically determined, and that all TFT's are obtained from one TFT by such perturbations. Several examples are presented, including twistedN=2 minimal topological matter and the case whereR is a group ring.     

Semi-classical theory of laser cooling in two dimensions

We present a semi-classical theory of the light pressure force for atoms interacting with a two-dimensional laser field. Unlike previous 2D theory, ours is valid for general atomic level and laser field configurations. We show that striking new features appear in the velocity-dependent force arising from the multi-dimensionality. Finally, we describe in detail the novel numerical technique used in the calculation. Received 4 December 1998 and Received in final form 13 February 1999     

Leading temperature corrections to Fermi-liquid theory in two dimensions

We calculate the basic parameters of the Fermi liquid: the scattering vertex, the Landau interaction function, the effective mass, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short-ranged interaction at nonzero temperature. The leading temperature dependences of the spin components of the scattering vertex, the Landau function, and the spin susceptibility are found to be linear. T-linear terms in the effective mass and in the "charge-sector" quantities are found to cancel to second order in the interaction, but the cancellation is argued not to be generic. The connection with previous studies of the 2D Fermi-liquid parameters is discussed.     

Kinetic theory of nonlinear viscous flow in two and three dimensions

On the basis of a nonlinear kinetic equation for a moderately dense system of hard spheres and disks it is shown that shear and normal stresses in a steady-state, uniform shear flow contain singular contributions of the form ¦X¦^3/2 for hard spheres, or ¦X¦ log ¦X¦ for hard disks. HereX is proportional to the velocity gradient in the shear flow. The origin of these terms is closely related to the hydrodynamic tails t^–d/2 in the current-current correlation functions. These results also imply that a nonlinear shear viscosity exists in two-dimensional systems. An extensive discussion is given on the range ofX values where the present theory can be applied, and numerical estimates of the effects are given for typical circumstances in laboratory and computer experiments.Supported by National Science Foundation grant No. CHE-73-08856 (to HvB, JRD, and JS) and the Center for Theoretical Physics of the Univ. of Md. (to HvB).On leave from Institute of Theoretical Physics, Warsaw University, Warsaw, Poland.     

Interacting fermions in two dimensions: beyond the perturbation theory

We consider a system of 2D fermions with a short-range interaction. A straightforward perturbation theory is shown to be ill defined even for an infinitesimally weak interaction, as the perturbative series for the self-energy diverges near the mass shell. We show that the divergences result from the interaction of fermions with the zero-sound collective mode. By resumming the most divergent diagrams, we obtain a closed form of the self-energy near the mass shell. The spectral function exhibits a threshold feature at the onset of the emission of the zero-sound waves. We also show that the interaction with the zero sound does not affect a nonanalytic, T2 part of the specific heat.     

Lattice versions of quantum field theory models in two dimensions

The quantum inverse scattering method allows one to put quantum field theory models on a lattice in a way which preserves the dynamical structure. The trace identifies are discussed for these models.     

Finite temperature λφ4 theory in two and three dimensions and symmetry restoration

λφ⁴ Theory is studied in 2 and 3 dimensions to examine the validity of the finite temperature perturbation theory. We find that in some cases it is good even at high temperature in contrast to the case in 4 dimensions. We also discuss the problem of symmetry restoration and show an example of symmetry restoration within a safe perturbation at high temperature.     

A relation between gauge-invariant formulation of QCD and string theory in two dimensions

We have studied the explicit relation between the gauge-invariant path-ordered operator (POO) and a string field in two dimensions. For this purpose, we use the hamiltonian of two-dimensional quantum chromodynamics reformulated in terms of POO. POO is expanded in a power series of a non-local bosonic operator. We show that such a bosonic operator describes Bars and Hanson's free string field in the second quantization. Interactions among bosonic operators are treated in perturbation theory. The coupling constant is proportional to 1/√N_c.     

Nonlocal current algebra and N = 2 superconformal field theory in two dimensions

We present a new construction of the unitary highest weight representations of the N = 2 superconformal algebras in two dimensions. This construction is based on the non-local current in the Z_N conformal theory and a free scalar field. It provides a physical realization of all the unitary N = 2 superconformal field theories by critical systems. The correlation functions of the theories can be calculated through this construction.     

Collapse of the electron gas to two dimensions in density functional theory

Local and semilocal density functional approximations for the exchange-correlation energy fail badly in the zero-thickness limit of a quasi-two-dimensional electron gas, where the density variation is rapid almost everywhere. Here we show that a fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sj?lander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover). We also show that this good behavior is only partly due to the use of the full exact exchange energy.     

A renormalizable field theory: The massive Gross-Neveu model in two dimensions

The Euclidean massive Gross-Neveu model in two dimensions is just renormalizable and asymptotically free. Thanks to the Pauli principle, bare perturbation theory with an ultra-violet cut-off (and the correct ansatz for the bare mass) is convergent in a disk, whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant. Therefore, the theory can be fully constructed in a perturbative way. It satisfies the O.S. axioms and is the Borel sum of the renormalized perturbation expansion of the model     

Existence of a phase transition in reggeon field theory in two transverse dimensions

We show that a reggeon field theory, in the physical number of dimensions, with a linear bare trajectory and a constant triple-pomeron coupling, undergoes a phase transition as the bare pomeron intercept is increased through a certain critical value.     

Intermediate statistics in two space dimensions in a lattice-regularized Hamiltonian quantum field theory

The non-compact Abelian Higgs model with a Chern-Simons term added is investigated within a Hamiltonian formalism, regularized by a spatial lattice. Transmutted matter fields are constructed, which show intermediate statistics interpolating continuously between the Bose and the Fermi case. Their unbounded localization properties are analyzed in detail. Moreover, the braid structure emerging, when exchanges in a product of transmuted fields are performed, is disclosed.