Second-quantized formulation of geometric phases

Adiabatic approximation in the second quantized formulation

Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and unambiguous criterion of the adiabatic approximation. This is illustrated for the model of Marzlin and Sanders and a model related to the geometric phase which...

On Second Geometric-Arithmetic Index of Graphs

The concept of geometric-arithmetic indices (GA) was put forward in chemical graph theory very recently. In spite of this, several works have already appeared dealing with these indices. In this paper we present lower and upper bounds on the second geometric-arithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish Nordhaus-Gaddum-type results for GA2.

Geometric Phases

Second Quantized Frobenius Algebras

We show that given a Frobenius algebra there is a unique notion of its second quantization, which is the sum over all symmetric group quotients of n–th tensor powers, where the quotients are given by symmetric group twisted Frobenius algebras. To this end, we consider the setting of Frobenius algebras given by functors from geometric categories whose objects are endowed with geometric group act...

Second-quantized Mirror Symmetry

We propose and give strong evidence for a duality relating Type II theories on CalabiYau spaces and heterotic strings on K3× T , both of which have N = 2 spacetime supersymmetry. Entries in the dictionary relating the dual theories are derived from an analysis of the soliton string worldsheet in the context of N = 2 orbifolds of dual N = 4 compactifications of Type II and heterotic strings. In ...