Related papers: Bargmann invariants and off-diagonal geometric pha…
We discuss a pairwise-comparison viewpoint on finite families of qubit states. Starting from transition amplitudes between pure states, we distinguish three associated levels of comparison data: complex amplitudes, transition probabilities,…
Geometrical phases have been applied in virtually every major branch of physics and they play an important role in topology and knot theory in mathematics and quantum computation. However, most of the early works focus on pure quantum…
In this article we consider the behavior in the vicinity of infinity of the class of all planar quadratic differential systems. This family depends on twelve parameters but due to action of the affine group and re-scaling of time the family…
The description of states and dynamics in non-Hermitian systems is fundamentally linked to the choice of an appropriate theoretical framework -- a point of ongoing debate in the field. This work addresses this issue by proposing a…
We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve…
A complete and rigorous determination of the possible ground states for D-wave pairing Bose condensates is presented, using a geometrical invariant theory approach to the problem. The order parameter is argued to be a vector, transforming…
We discuss the topology of the parameter space of invertible phases with an onsite symmetry $G$, i.e., quantum many-body ground states that have neither fractionalization nor spontaneous breaking of the symmetry. The classification of…
The gauge invariance of geometric phases for mixed states is analyzed by using the hidden local gauge symmetry which arises from the arbitrariness of the choice of the basis set defining the coordinates in the functional space. This…
Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently…
We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer…
We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer…
Neutrinos can acquire both dynamic and geometric phases due to the non-trivial mixing between mass and flavour eigenstates. In this article, we derive the general expressions for all plausible gauge invariant diagonal and off-diagonal…
The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in…
We consider SPT-phases with on-site finite group $G$ symmetry for two-dimensional Fermion systems.We derive an invariant of the classification.
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
Set coherence is a basis-independent relational form of quantum coherence: a finite family of quantum states is set incoherent exactly when all its members are diagonal in one common basis. We determine how much low-order Bargmann data are…
The geometric and open path phases of a four-state system subject to time varying cyclic potentials are computed from the Schr\"{o}dinger equation. Fast oscillations are found in the non-adiabatic case. For parameter values such that the…
Geometric phases play a fundamental role in understanding quantum topology, yet extending the Uhlmann phase to non-Hermitian systems poses significant challenges due to parameter-dependent inner product structures. In this work, we develop…
The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…