Related papers: Quantum geometric bounds for observables: Linear r…
We study the effect of quantum geometry on the many-body ground state of one-dimensional interacting bosonic systems. We find that the Drude weight is given by the sum of the kinetic energy and a term proportional to the many-body quantum…
We extend the quantum geometric tensor from the state space to the operator level,and investigate its properties like the additivity for factorizable models and the splitting of two kinds contributions for the case of stationary reference…
We assess two different non-equilibrium quantum Landauer bounds: the traditional approach based on the change in entropy, referred to as the `entropic bound', and one based on the details of the dynamical map, referred to as the…
Phenomenological approaches to quantum gravity try to infer model-independent laws by analyzing thought experiments and combining both quantum, relativistic, and gravitational ingredients. We first review these ingredients -three basic…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
We study classical limit for quantum mechanics with two times and temperature, which describes a generalized dynamics of relativistic point mass. In this theory, thermodynamic time means a parameter of evolution, whereas geometric time is…
In this paper, we extend the quantum geometric tensor for parameter-dependent curved spaces to higher dimensions, and introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the tensor. The parameter-dependent…
Quantum geometry provides important information about the structure and topology of quantum states in various forms of quantum matter. The information contained therein has profound effects on observable quantities such as superconducting…
We specify bulk coordinates in Jackiw-Teitelboim (JT) gravity using a boundary-intrinsic radar definition. This allows us to study and calculate exactly diff-invariant bulk correlation functions of matter-coupled JT gravity, which are found…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
We examine the conditions under which the thermodynamic behaviour of gravity can be explained within an emergent gravity scenario, where the metric is defined as a composite operator. We show that due to the availability of a boundary of a…
In this paper we investigate the bound state problem of nonrelativistic quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we…
Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian is the boundary term required by functional differentiability of the action for…
We propose a novel framework for the quantum geometry of expectation values over arbitrary sets of operators and establish a link between this geometry and the eigenstates of Hamiltonian families generated by these operators. We show that…
The quantum metric tensor was introduced for defining the distance in the parameter space of a system. However, it is also useful for other purposes, like predicting quantum phase transitions. Due to the physical information this tensor…
Quantum entanglement between several particles is essential for applications like quantum metrology or quantum cryptography, but it is also central for foundational phenomena like quantum non-locality. This leads to the problem of…
We study the boundary correlation functions in Liouville theory and in solvable statistical models of 2D quantum gravity. In Liouville theory we derive functional identities for all fundamental boundary structure constants, similar to the…
An equidistant spectrum of the horizon area of a quantized black hole does not follow from the correspondence principle or from general statistical arguments. On the other hand, such a spectrum obtained in loop quantum gravity (LQG) either…
Quantifying quantum entanglement is a pivotal challenge in quantum information science, particularly for high-dimensional systems, due to its computational complexity. This thesis extends the geometric measure of entanglement (GME) to…
We analyze the algebra of observables of a charged particle on a noncommutative torus in a constant magnetic field. We present a set of generators of this algebra which coincide with the generators for a commutative torus but at a different…