Related papers: Semiclassical Wave-Packet Dynamics in Phase-Space …
Quantum geometry quantifies how the single-particle Bloch wavefunction changes in phase and amplitude across the Brillouin Zone. In multi-orbital systems where bands have strongly mixed orbital composition, quantum geometry plays a vital…
We study the magnetic Bloch oscillations performed by a quantum particle moving in a two-dimensional lattice in the presence of a strong (synthetic) magnetic field and a uniform force. An elementary derivation of the Berry curvature effect…
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
An isolated classical chaotic system, when driven by the slow change of several parameters, responds with two reaction forces: geometric friction and geometric magnetism. By using the theory of quantum fluctuation relations we show that…
Simulation and analysis of multidimensional dynamics of a quantum non-Hmeritian system is a challenging problem. Gaussian wavepacket dynamics has proven to be an intuitive semiclassical approach to approximately solving the dynamics of…
In the literature, there are several papers establishing a correspondence between a deformed kinematics and a nontrivial (momentum dependent) metric. In this work, we study in detail the relationship between the trajectories given by a…
The possibilities of curvature of space-time in the metric of quantum states are investigated. The curvature of the metric corresponding to a wave function of Hydrogen atom is determined. Also, Einstein tensor is described for a given…
We study quantum aspects of the Einstein gravity with one time-like and one space-like Killing vector commuting with each other. The theory is formulated as a $\coset$ nonlinear $\sigma$-model coupled to gravity. The quantum analysis of the…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
The eigenvalues of a parameter-dependent Hamiltonian matrix form a band structure in parameter space. In such $N$-band systems, the quantum geometric tensor (QGT), consisting of the Berry curvature and quantum metric tensors, is usually…
We construct a theory for the semiclassical dynamics of superconducting quasiparticles by following their wave-packet motion and reveal rich contents of Berry curvature effects in the phase-space spanned by position and momentum. These…
Time-dependent $\mathcal{PT}$-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
The quantum geometric properties of typical diamond-type (C, Si, Ge) and zincblende-type (GaAs, InP, etc) semiconductors are investigated by means of the $sp^{3}s^{\ast}$ tight-binding model, which allows to calculate the quantum metric of…
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play…
Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the…
The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…
Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field…