Related papers: Laughlin states change under large geometry deform…
It is conjectured that the spatial structure of quantum field states is influenced by a new kind of directional indeterminacy of quantum geometry set by the Planck length, $l_P$, that does not occur in a classical background geometry.…
The fractional quantum Hall (FQH) effect is one of the most striking phenomena in condensed matter physics. It is described by a simple Laughlin wavefunction and has been thoroughly studied both theoretically and experimentally. In lattice…
A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems.…
We revisit pure quantum cosmology in three dimensions. The Wheeler-DeWitt equation can be solved perturbatively and the dynamics reduces to a particle on moduli space. Its time evolution is equivalent to the $T\overline{T}$ deformation.…
The evolution of a quantum system is governed by the associated Hamiltonian. A system defined by a parameter-dependent Hamiltonian acquires a geometric phase when adiabatically evolved. Such an adiabatic evolution of a system having…
We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous K\"ahler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in…
We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same method in the case of SU(3) we study…
Quantum mechanical phase factors can be related to dynamical effects or to the geometrical properties of a trajectory in a given space - either parameter space or Hilbert space. Here, we experimentally investigate a quantum mechanical phase…
Strongly interacting systems are characterized by heavily dressed entities with internal degrees of freedom, which, on a local level, can be described in terms of coherent quantum states. We examine the modification of these local coherent…
A distinguishing feature of fractional quantum Hall (FQH) states is a singular behavior of equilibrium densities at boundaries. In contrast to states at integer filling fraction, such quantum liquids posses an additional dipole moment…
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
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…
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
We consider the generic problem of suddenly changing the geometry of an integrable, one-dimensional many-body quantum system. We show how the physics of an initial quantum state released into a bigger system can be completely described…
Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various…
Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude $S$ have $N=2S+1$ levels. Alternatively, the spin state is fully…
We investigate fast rotating quasi-two-dimensional dipolar Fermi gases in the quantum Hall regime. By tuning the direction of the dipole moments with respect to the z-axis, the dipole-dipole interaction becomes anisotropic in the $x$-$y$…
Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a…
The discovery of topological matter has revolutionized the field of condensed matter physics giving rise to many interesting phenomena, and fostering the development of new quantum technologies. In this thesis we study the quantum dynamics…