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Algebraic methods for solving time dependent Hamiltonians are used to investigate the performance of quantum thermal machines. We investigate the thermodynamic properties of an engine formed by two coupled q-bits, performing an Otto cycle.…
We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally…
Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. Using this insight, we develop a geometric framework to describe its time evolution. In particular, we identify mutually orthogonal coherent and…
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…
Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work we consider time-periodically modulated quantum systems which are in contact with a stationary…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
Here, we develop the exact dynamics of the central spin model, modeling a finite-bath open quantum system. Particularly, two different types of interactions are investigated between the system and the bath: Heisenberg interaction with…
Many-body quantum systems present a rich phenomenology which can be significantly altered when they are in contact with an environment. In order to study such setups, a number of approximations are usually performed, either concerning the…
The geometric (Berry) phase of a two-level system in a dissipative environment is analyzed by using the second-quantized formulation, which provides a unified and gauge-invariant treatment of adiabatic and nonadiabatic phases and is thus…
We describe the decoherence process induced on a two-level quantum system in direct interaction with a non-equilibrium environment. The non-equilibrium feature is represented by a non-stationary random function corresponding to the…
When the coupling of a quantum system to its environment is non-negligible, its steady state is known to deviate from the textbook Gibbs state. The Bloch-Redfield quantum master equation, one of the most widely adopted equations to solve…
This work is a pedagogical survey about the hierarchical equations of motion and their implementation with the tensor-train format. These equations are a great standard in non-perturbative non-Markovian open quantum systems. They are exact…
We provide a theoretical model for the non-equilibrium steady state heat flow through a quantum heat valve. The model is based on a master equation approach, where the partial secular approximation has been carefully performed in order to…
We propose a method which combines the quantum-classical mapping approach to surface hopping (MASH) with the dissipative quantum dynamics of the Lindblad master equation. Like conventional surface-hopping methods, our approach is based on…
We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…
Quantum computing offers promising new avenues for tackling the long-standing challenge of simulating the quantum dynamics of complex chemical systems, particularly open quantum systems coupled to external baths. However, simulating such…
We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different…
In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such a system where the Liouvillian is mapped to an XXZ Richardson-Gaudin integrable model and detail its…
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial…
We show how to recover complete positivity (and hence positivity) of the Redfield equation via a coarse grain average technique. We derive general bounds for the coarse graining time scale above which the positivity of the Redfield equation…