# All

Symmetry is one of the most general and useful concepts in physics. A theory

or a system that has a symmetry is fundamentally constrained by it. The same

constraints do not apply when the symmetry is broken. The quantitative

determination of "how much a system breaks a symmetry" allows to reach beyond

this binary situation and is a necessary step towards the quantitative

connection between symmetry breaking and its effects. We introduce measures of

symmetry breaking for a system interacting with external fields (particles).

Observables have a dual nature in both classical and quantum kinematics: they

are at the same time \emph{quantities}, allowing to separate states by means of

their numerical values, and \emph{generators of transformations}, establishing

relations between different states. In this work, we show how this two-fold

role of observables constitutes a key feature in the conceptual analysis of

classical and quantum kinematics, shedding a new light on the distinguishing

We propose a noisy quantum analogue of the well known Stuart--Landau equation

for weakly nonlinear oscillators. Surprisingly, we find the oscillator's

amplitude to be amplified by the very same noise responsible for its stochastic

dynamics. This has interesting implications for the theory of linear amplifiers

and the so-called quantum van der Pol model used in quantum synchronisation. We

then go beyond the weakly nonlinear regime and obtain an exact quantum analogue

We introduce the coherent state mapping ring-polymer molecular dynamics

(CS-RPMD), a new method that accurately describes electronic non-adiabatic

dynamics with explicit nuclear quantization. This new approach is derived by

using coherent state mapping representation for the electronic degrees of

freedom (DOF) and the ring-polymer path-integral representation for the nuclear

DOF. CS-RPMD Hamiltonian does not contain any inter-bead coupling term in the

state-dependent potential, which is a key feature that ensures correct

Since the enlightening proofs of quantum contextuality first established by

Kochen and Specker, and also by Bell, various simplified proofs have been

constructed to exclude the non-contextual hidden variable theory of our nature

at the microscopic scale. The conflict between the non-contextual hidden

variable theory and quantum mechanics is commonly revealed by Kochen-Specker

(KS) sets of yes-no tests, represented by projectors (or rays), via either

logical contradictions or noncontextuality inequalities in a

To investigate frequency-dependent current noise (FDCN) in open quantum

systems at steady states, we present a theory which combines Markovian quantum

master equations with a finite time full counting statistics. Our formulation

of the FDCN generalizes previous zero-frequency expressions and can be viewed

as an application of MacDonald's formula for electron transport to heat

transfer. As a demonstration, we consider the paradigmatic example of quantum

Applying a many mode Floquet formalism for magnetically trapped atoms

interacting with a polychromatic rf-field, we predict a large two photon

transition probability in the atomic system of cold $^{87}Rb$ atoms. The

physical origin of this enormous increase in the two photon transition

probability is due to the formation of avoided crossings between eigen-energy

levels originating from different Floquet sub-manifolds and redistribution of

population in the resonant intermediate levels to give rise to the resonance

We use a self-assembled two-dimensional Coulomb crystal of $\sim 70$ ions in

the presence of an external transverse field to engineer a quantum simulator of

the Dicke Hamiltonian. This Hamiltonian has spin and bosonic degrees of freedom

which are encoded by two hyperfine states in each ion and the center of mass

motional mode of the crystal, respectively. The Dicke model features a quantum

critical point separating two distinct phases: the superradiant (ferromagnetic)

SrTiO3-based heterointerfaces support quasi-two-dimensional (2D) electron

systems that are analogous to III-V semiconductor heterostructures, but also

possess superconducting, magnetic, spintronic, ferroelectric and ferroelastic

degrees of freedom. Despite these rich properties, the relatively low

mobilities of 2D complex-oxide interfaces appear to preclude ballistic

transport in 1D. Here we show that nearly ideal 1D electron waveguides

exhibiting quantized ballistic transport of electrons and (non-superconducting)

Non-Hermitian systems with parity-time symmetry have been developed rapidly

and hold great promise for future applications. Unlike most existing works

considering the symmetry of the free energy terms (e.g., gain-loss system), in

this paper, we report that a realizable non-Hermitian interaction between two

quantum resonances can also have a real spectrum after the exceptional point.

That phenomenon is similar with that in the gain-loss system so that the