Related papers: Exploring Many-Body Quantum Geometry Beyond the Qu…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
Quantum geometry characterizes the variation of wavefunctions in momentum space through their overlaps and relative phases, providing a general framework for understanding many transport and optical properties. It is generally formulated in…
We study the geodesics on the manifold of mixed quantum states for the Bures metric. It is shown that these geodesics correspond to physical non-Markovian evolutions of the system coupled to an ancilla. Furthermore, we argue that geodesics…
The geometry of the parameter space is encoded by the quantum geometric tensor, which captures fundamental information about quantum states and contains both the quantum metric tensor and the curvature of the Berry connection. We present a…
The aim of this paper is to provide a largely self-contained, compact and comprehensible introduction to the basic ideas behind correlation geometry, which underlies the theory of causal fermion system (CFS). A key focus here is on 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…
There has been much work in the recent past in developing the idea of quantum geometry to characterize and understand the structure of many-particle states. For mean-field states, the quantum geometry has been defined and analysed in terms…
We evaluate the density matrix of an arbitrary quantum mechanical system in terms of the quantities pertinent to the solution of the time-dependent density functional theory (TDDFT) problem. Our theory utilizes the adiabatic connection…
Microscopically probing quantum many-body systems by resolving their constituent particles is essential for understanding quantum matter. In most physical systems, distinguishing individual particles, such as electrons in solids, or…
We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the…
We introduce the concept of quantum weight as a ground state property of quantum many-body systems that is encoded in the static structure factor and characterizes density fluctuation at long wavelengths. The quantum weight carries a wealth…
The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…
We develop a multi affine geometric framework to unify classical and quantum mechanical laws through the lens of information geometry. By combining the principle of stationary action with maximum entropy production, we show that divergences…
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to…
Knowledge of all correlation functions of a system is equivalent to solving the corresponding many-body problem. Already a finite set of correlation functions can be sufficient to describe a quantum many-body system if correlations…
The apparent randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations dynamically imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions…
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…
Berry phases and gauge structures in parameter spaces of quantum systems are the foundation of a broad range of quantum effects such as quantum Hall effects and topological insulators. The gauge structures of interacting many-body systems,…
The traditional formalism of non-relativistic quantum theory allows the state of a quantum system to extend across space, but only restricts it to a single instant in time, leading to distinction between theoretical treatments of spatial…