相关论文: Gauge invariants of eigenspace and eigenvalue anho…

Various phenomena related to geometric phases in quantum mechanics are reviewed and explained by analyzing some examples.The concepts of 'parallelism' ,'connections' and 'curvatures' are applied to Aharonov-Bohm (AB) effect, to U(1)phase…

Although axial QED suffers from a gauge anomaly, gauge invariance may be maintained by the addition of a nonlocal counterterm. Such nonlocal conterterms, however, are expected to ruin unitarity of the theory. We explicitly investigate some…

In these lecture notes, partly based on a course taught at the Karpacz Winter School in March 2014, we explore the close connections between non-adiabatic response of a system with respect to macroscopic parameters and the geometry of…

We present both the gauge theoretic description and the numerical calculations of the Berry phases with the real eigenstates, involving one with a many-body system as a background and the other with no such background. We demonstrate that…

The geometry of Hamiltonian's eigenstates is encoded in the quantum geometric tensor (QGT). It contains both the Berry curvature, central to the description of topological matter and the quantum metric. So far the full QGT has been measured…

Recently there has been much interest in gauge theories applied to condensed matter physics. I show that for a system of nonrelativistic electrons coupled to a U(1) gauge field in the presence of a Fermi surface, the beta-function to…

The Aharonov-Bohm effect has been invoked to probe the phase structure of a gauge theory. Yet in the case of non-Abelian gauge theories, it proves difficult to formulate a general procedure that unambiguously specifies the realization of…

The two ways of constrained systems quantization are considered from the point of view of their self-consistency at the quantum level. With a transparent example of a particle in the external electromagnetic field we demonstrate that the…

The problem of gauge invariance in an ultraviolet complete quantum field theory (QFT) with nonlocal interactions is investigated. For local fields that couple through a nonlocal interaction, it is demonstrated that the quantum…

We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices…

We consider the semiclassical equations of motion of a particle when both an external electromagnetic field and the Berry gauge field in the momentum space are present. It is shown that these equations are Hamiltonian and relations between…

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint…

Given a parameterized space of square matrices, the associated set of eigenvectors forms some kind of a structure over the parameter space. When is that structure a vector bundle? When is there a vector field of eigenvectors? We answer…

We derive the effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) in the asymptotic limit where the restoring forces tend to infinity. In contrast to…

Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent…

In BV formalism we can consider a Lagrangian submanifold as a gauge condition. Starting with the BV action functional we construct a closed form on the space of Lagrangian submanifolds. If the action functional is invariant with respect to…

We investigate lattice and continuous quantum gauge theories on the Euclidean plane with a structure group that is replaced by a $H$-algebra; non-commutative analogues of groups and contain the class of Voiculescu's dual groups. We are…

Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits…

A complete basis of nonlocal invariants in quantum gravity theory is built to third order in spacetime curvature and matter-field strengths. The nonlocal identities are obtained which reduce this basis for manifolds with dimensionality…

Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an…