相关论文: Hessian Geometry and Phase Changes of Multi-Taub-N…

We study the geometry of the Thurston metric on the Teichm\"uller space $\mathcal{T}(S)$ of hyperbolic structures on a surface $S$. Some of our results on the coarse geometry of this metric apply to arbitrary surfaces $S$ of finite type;…

The geometrical approach to phase transitions is illustrated by simulating the high-temperature representation of the Ising model on a square lattice.

We discuss several bosonic topological phases in (3+1) dimensions enriched by a global $\mathbb{Z}_2$ symmetry, and gauging the $\mathbb{Z}_2$ symmetry. More specifically, following the spirit of the bulk-boundary correspondence, expected…

We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase…

We consider $G_2$-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of $T^3$-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the…

We propose a generalized quantum geometric tenor to understand topological quantum phase transitions, which can be defined on the parameter space with the adiabatic evolution of a quantum many-body system. The generalized quantum geometric…

We analyze the geometry on the space of non-unital phase-covariant qubit maps. Using the corresponding Choi-Jamio{\l}kowski states, we derive the Hilbert-Schmidt line and volume elements using the channel eigenvalues together with the…

We examine the dynamic and geometric phases of the electron in quantum mechanics using Hestenes' spacetime algebra formalism. First the standard dynamic phase formula is translated into the spacetime algebra. We then define new formulas for…

This paper studies the quantization of the deformation of Hessian structures on a two-dimensional vector space, in the framework of Koszul-Vinberg algebras. We analyze how Hessian structures can be deformed to obtain quantum structures…

The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \emph{homological type} of a geometric transition. The obtained results agree…

The relation between the geometric phase and quantum phase transition has been discussed in the Lipkin-Meshkov-Glick model. Our calculation shows the ability of geometric phase of the ground state to mark quantum phase transition in this…

We introduce a generalization of Taub-NUT deformations for large families of hyper-Kaehler quotients including toric hyper-Kaehler manifolds and quiver varieties, and apply them to the case of the Hilbert schemes of k points on C^2.

Recently proposed forms for gauge transformations with finite parameters in double field theory are discussed and problematic issues are identified. A new form for finite gauge transformations is derived that reveals the underlying gerbe…

We study information geometry of the thermodynamics of first and second order phase transitions, and beyond criticality, in magnetic and liquid systems. We establish a universal microscopic characterization of such phase transitions via the…

A teleparallel geometrical description of the nematic phases of liquid crystals is proposed.In the case of the twisted geometry of nematics Cartan torsion is given by a spatial helical form which depends on the twist angle. Geodesics of a…

We review the recent theoretical developments towards understanding the Mott phases and quantum phase transition of extended Bose-Hubbard models on lattices in two spatial dimensions . We focuss on the description of these systems using the…

Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic…

We study general models for holographic superconductors in Einstein-Gauss-Bonnet gravity. We find that different values of Gauss-Bonnet correction term and model parameters can determine the order of phase transitions and critical exponents…

A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…

This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…