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