Related papers: An Elementary Characterization of Bargmann Invaria…
A bicovariant calculus on the twisted inhomogeneous multiparametric $q$-groups of the $B_n,C_n,D_n$ type, and on the corresponding quantum planes, is found by means of a projection from the bicovariant calculus on $B_{n+1}$, $C_{n+1}$,…
Weak values, obtained from weak measurements, attempt to describe the properties of a quantum system as it evolves from an initial to a final state, without practically altering this evolution. Trajectories can be defined from weak…
In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants associates an irreducible representation…
In [BF12] the authors associated to a knot K an invariant n_R(K) which is defined using the Blanchfield form and which gives a lower bound on the unknotting number. In this paper we express n_R(K) in terms of Levine-Tristram signatures and…
We show that higher order inter-group covariances involving even number of qubits are necessarily positive semidefinite for N qubit separable states, which are completely symmetric under permutations of the qubits. This identification leads…
This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
We examine shape invariant potentials (excluding those that are obtained by scaling) in supersymmetric quantum mechanics from the stand-point of periodic orbit theory. An exact trace formula for the quantum spectra of such potentials is…
In a system of n quantum particles, we define a measure of the degree of irreducible n-way correlation, by which we mean the correlation that cannot be accounted for by looking at the states of (n-1) particles. In the case of almost all…
The importance of simple geometrical invariants, such as the Berry curvature and quantum metric, constructed from the Bloch states of a crystal has become well-established over four decades of research. More complex aspects of geometry…
Meaningful topological invariants for mixed quantum states are challenging to identify as there is no unique way to define them, and most choices do not directly relate to physical observables. Here, we propose a simple pragmatic approach…
Manifestly covariant formalism for Bargmann-Wigner fields is developed. It is shown that there exists some freedom in the choice of the form of the Bargmann-Wigner scalar product: The general product depends implicitly on a family of…
We define invariants for a framed link equipped with a SL2 local system in its complement and additional combinatorial data based on the theory of representations of stated skein algebras at roots of unity of punctured bigons and the…
Topological phases of materials are characterized by topological invariants that are conventionally calculated by different means according to the dimension and symmetry class of the system. For topological materials described by Dirac…
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly…
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…
Gauge invariance is a fundamental principle that must be preserved in quantum transport. However, when a complex potential is incorporated into the Hamiltonian, we find that the current described by the well-established…
We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the…
A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be…
A new path integral approach of quantum gravity based on relational variables and quantum test objects is presented. We take as a basic variables the squared invariant distance. This invariant quantity is technically simpler to work with…