Related papers: Hessian Geometry and Phase Change of Gibbons-Hawki…
We study the thermodynamic geometry of the Quark-Meson model, focusing on the curvature, $R$, around the chiral crossover at finite temperature and baryon chemical potential. We find a peculiar behavior of $R$ in the crossover region, in…
Geometric phase is a key player in many areas of quantum science and technology. In this review article, several foundational aspects of quantum geometric phases and their relations to classical geometric phases are outlined. How the…
We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional…
Beyond the quantum Markov approximation, we calculate the geometric phase of a two-level system driven by a quantized magnetic field subject to phase dephasing. The phase reduces to the standard geometric phase in the weak coupling limit…
We study how the length and the twisting parameter of a curve change along a Teichmuller geodesic. We then use our results to provide a formula for the Teichmuller distance between two hyperbolic metrics on a surface, in terms of the…
We report on the recent results revealing the presence of geometric invariants in all the phenomena in which vacuum condensates appear and we show that Aharonov--Anandan phase can be used to provide the evidence of phenomena like Hawking…
Geometric entanglement(GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. We outline a systematic method to compute GE for…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
We study the electroweak phase transition in an effective 3-dimensional theory for a Higgs mass of about 70 GeV by Monte Carlo simulations. The transition temperature and jumps of order parameters are obtained and extrapolated to the…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also…
Geometrical and topological phases play a fundamental role in quantum theory. Geometric phases have been proposed as a tool for implementing unitary gates for quantum computation. A fractional topological phase has been recently discovered…
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…
Numerical simulations are performed to study the finite temperature phase transition in the SU(2) Higgs model on the lattice. In the presently investigated range of the Higgs boson mass, below 50 GeV, the phase transition turns out to be of…
When subject to measurements, quantum systems evolve along stochastic quantum trajectories that can be naturally equipped with a geometric phase observable via a post-selection in a final projective measurement. When post-selecting the…
Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric…
We extend the correspondence between Hessian and K\"ahler metrics and curvatures to Lagrange spaces.
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…