Related papers: Nonadiabatic quantum geometry and optical conducti…
We define for quantum many-body systems a quasi-adiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density of states, and thus is away from a…
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are…
Mixed-quantum-classical molecular dynamics simulation implies an effective measurement on the electronic states owing to continuously tracking the atomic forces.Based on this insight, we propose a quantum trajectory mean-field approach for…
The quantum geometric tensor (QGT) is a fundamental concept for characterizing the local geometry of quantum states. After casting the geometry of pure quantum states and extracting the QGT, we generalize the geometry to mixed quantum…
The optical conductivity is the basic defining property of materials characterizing the current response toward time-dependent electric fields. In this work, following the approach of Kubo's response theory, we study the general properties…
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
Adiabatic quantum computation (AQC), which is particularly useful for combinatorial optimization, becomes more powerful by using excited states, instead of ground states. However, the excited-state AQC is prone to errors due to dissipation.…
Quantum computation has demonstrated advantages over classical computation for special hard problems, where a set of universal quantum gates is essential. Geometric phases, which have built-in resilience to local noise, have been used to…
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…
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This…
The geometric phase stands as a foundational concept in quantum physics, revealing deep connections between geometric structures and quantum dynamical evolution. Unlike dynamical phases, geometric phases exhibit intrinsic resilience to…
Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully…
We study the adiabatic dynamics of degenerate quantum states induced by loop paths in a control parameter space. The latter correspond to noisy trajectories if the system is weakly coupled to environmental modes. On top of conventional…
In loop quantum gravity, states of the gravitational field turn out to be excitations over a vacuum state that is sharply peaked on a degenerate spatial geometry. While this vacuum is singled out as fundamental due to its invariance…
We investigate the geometry of a quantum universe with the topology of the four-torus. The study of non-contractible geodesic loops reveals that a typical quantum geometry consists of a small semi-classical toroidal bulk part, dressed with…
The quantum geometric tensor (QGT) is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena. The traditional QGT, defined only for pure…
In this paper, Non-Equilibrium Steady State induced by electric field and the conductivity of non-interacting fermion systems under the dissipative dynamics is discussed. The dissipation is taken into account within a framework of the…
Models of quantum computation are important because they change the physical requirements for achieving universal quantum computation (QC). For example, one-way QC requires the preparation of an entangled "cluster" state followed by…