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The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
The paper is the first of two parts of the work devoted to the investigation of constructing quantum theory of a closed universe as a system without asynptotic states. In Part I the role of asymptotic states in quantum theory of gravity is…
Nonadiabatic dressed states of a quantum system interacting with an external electromagnetic field and the environment are presented. The relevant matrix elements within the specified states are found. A closed form expression of the…
Quantum geometry, including quantum metric and Berry curvature, which describes the topology of electronic states, can induce fascinating physical properties. Symmetry-dependent nonlinear transport has emerged as a sensitive probe of these…
We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
Quantum algorithms are prominent in the pursuit of achieving quantum advantage in various computational tasks. However, addressing challenges, such as limited qubit coherence and high error rate in near-term devices, requires extensive…
Appearance of adiabatic geometric phase shift in the context of noncommutative quantum mechanics is studied using an exactly solvable model of 2D simple harmonic oscilator in Moyal plane, where momentum non-commutativity are also considered…
We present a general unified approach for the study of quantum thermal machines, including both heat engines and refrigerators, operating under periodic adiabatic driving and in contact with thermal reservoirs kept at different…
It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of…
In this work, we deepen the correspondence between Generalized Uncertainty Principles (GUPs) and quantum dynamics on curved momentum space. In particular, we investigate the linear and quadratic GUP. Similarly to earlier work, the resulting…
The importance of the quantum metric in flat-band systems has been noticed recently in many contexts such as the superfluid stiffness, the dc electrical conductivity, and ideal Chern insulators. Both the quantum metric of degenerate and…
We investigate the quantum aspects of three-dimensional gravity with a positive cosmological constant. The reduced phase space of the three-dimensional de Sitter gravity is obtained as the space which consists of the Kerr-de Sitter…
It is well known that noncommutative geometry naturally emerges in the quantum Hall states due to the presence of strong and constant magnetic fields. Here, we discuss the underlying noncommutative geometry of quantum Hall fluids in which…
We generalize the perturbations theory of loop quantum cosmology to a hydrodynamical form and define an effective curvature perturbation on an uniform density hypersurfaces $\zeta_e$. As in the classical cosmology, $\zeta_e$ should be…
Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling…
Quantum computation has revolutionary potential for speeding algorithms and for simulating quantum systems such as molecules. We report here a quantum computer design that performs universal quantum computation within a single…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
We study geometric properties of a random Gaussian short-time correlated velocity field by considering statistics of a passively advected metric tensor. That describes universal properties of fluctuations of tensor objects frozen into the…
Quantum de Sitter geometry is discussed using elementary field operator algebras in Krein space quantization from an observer-independent point of view, {\it i.e.} ambient space formalism. In quantum geometry, the conformal sector of the…