arXiv subjects

Marta Reboiro

Publications and source records attributed to Marta Reboiro.

12 recordsLinked to original sources

arXiv2026

Bounded Dyson maps and cavity-driven transitions in a time-dependent non-Hermitian spin-boson model

We study a time-dependent non-Hermitian extension of the Schütte-Da Providência spin-boson Hamiltonian with complex couplings. A time-dependent Dyson map relates the model to a Hermitian counterpart and induces a positive physical metric. Separating the positive and unitary parts of the map, we prove a no-go result for a natural Gaussian number-squeeze-number class: for a nonvanishing linear spin-boson interaction, Hermiticity and bounded invertibility force the entire bosonic part of the Dyson map to be unitary. The squeezing parameter therefore selects a time-dependent Hermitian frame rather than contributing to the metric. The squeezed and non-squeezed Hamiltonians are related exactly by a time-dependent unitary transformation. The conserved quantity formed from the boson number and spin projection is replaced by a transported dynamical invariant, so a closed squeezing-frame protocol cannot generate transitions between distinct invariant sectors. We then introduce an independently driven single-mode cavity with quadratic term $iχ(t)(b^{\dagger2}-b^2)/2$. This physical drive breaks the corresponding continuous symmetry while preserving parity and couples dressed sectors differing by two bosonic quanta. The non-Hermitian asymmetry parameter, which also determines the bounded metric, tunes the effective Hermitian coupling, transition strengths and resonance conditions. Direct numerical propagation confirms the distinction between passive frame-induced mixing and genuine cavity transitions, the asymmetry-controlled resonance shift, and the validity of the first-order transition formula in the weak-driving regime.

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arXiv2026

Driving collective RPA modes by a time-dependent Dyson map

We study a time-dependent non-Hermitian generalisation of the Schütte-Da~Providência model describing a bosonic mode coupled to collective particle-hole excitations. Using a time-dependent Dyson map, we construct a Hermitian counterpart and reduce the collective fermionic sector by means of the random phase approximation (RPA). The resulting dynamics is mapped to two time-dependent harmonic-oscillator branches with instantaneous RPA frequencies $W_\pm(t)$. We determine the corresponding stability regions and compute transition probabilities between instantaneous oscillator states. In first-order instantaneous-basis perturbation theory the leading transition $n\to n+2$ is proportional to $\dot W_j/W_j$, showing that it is purely nonadiabatic and absent in the time-independent case. We compare this result with exact Lewis-Riesenfeld transition amplitudes within the RPA approximation. Numerical examples show that different components of the Dyson map provide distinct driving mechanisms: the scaling parameter modulates the effective coupling, while the squeezing parameter acts through a moving-boundary contribution. In both cases the induced collective transitions exhibit parametric-resonance peaks and sideband structures.

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arXiv2026

Out-of-time-order correlators for Swanson Hamiltonian with interaction terms

In this work, we compute the out-of-time-ordered correlator (OTOC) for canonical position and momentum operators across a hierarchy of non-Hermitian oscillator models: the exactly solvable Swanson Hamiltonian, its Kerr-nonlinear extension, and parametrically driven variants. By employing the biorthogonal formalism required for parity-time symmetric quantum mechanics, we evaluate OTOCs both at zero and finite temperature, distinguishing behavior in the unbroken (real-spectrum) and broken (complex-spectrum) phases. Our analysis reveals how integrability, nonlinearity, driving, and parity-time symmetry breaking shape the temporal growth of operator correlations -- providing a clear benchmark for OTOC dynamics in non-Hermitian quadratic and weakly anharmonic systems. We further characterize critical scaling of the OTOC near the exceptional point and discuss experimental perspectives for observing these effects in photonic, circuit-QED, and trapped-ion platforms.

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arXiv2026

Uncertainty inequalities in a non-Hermitian scenario

We investigate uncertainty relations for quantum observables evolving under non-Hermitian Hamiltonians, with particular emphasis on the role of metric operators. By constructing appropriate metrics in each dynamical regime, namely the unbroken-symmetry phase, the spontaneously broken-symmetry phase, and at exceptional points, we provide a consistent definition of expectation values, variances, and time evolution within a Krein-space framework. Within this approach, we derive a generalized Heisenberg-Robertson uncertainty inequality which is valid across all spectral regimes. As an application, we analyze a spin model with parity-time reversal symmetry and show that, while the uncertainty measure exhibits oscillatory behavior in the unbroken phase, it evolves towards a minimum-uncertainty steady state in the spontaneously broken-symmetry phase and at exceptional points. We further compare our metric-based description with a Lindblad master-equation approach and show their agreement in the steady state. Our results highlight the necessity of incorporating appropriate metric structures to extract physically meaningful predictions from non-Hermitian quantum dynamics.

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arXiv2025

A Pseudo-Hermitian Hybrid Model at Finite Temperature: The Role of the Exceptional Points

We study a hybrid system formed by an ensemble of colour nitrogen-vacancy centres in diamond interacting with a superconducting flux-qubit at finite temperature. The presence of impurities in the system is modelled through pseudo-hermitian Hamiltonian, by introducing an asymmetry parameter in the interaction between the superconducting flux qubit and the ensemble of colour nitrogen-vacancy centres in diamond. We construct the exact grand partition function of the system, and from it we derive the thermodynamic quantities, e.g. entropy, internal energy, and Helmholtz free energy. In the broken symmetry phase, we observe the existence of zeros in the partition function. These zeros are related to the existence of complex-pair-conjugate eigenvalues with real parts lying among the low levels of energy. In line with the Yang-Lee framework, these zeros in the complex plane signal phase transitions, and the proposed hybrid model exhibits transitions of first-order. To account for metastable regions in parameter space, we perform a Maxwell construction and a spinodal-decomposition analysis. We determine the critical temperature at which the first zero of the partition-function appears, as a function of the asymmetry parameter and the coupling constant of the interaction between the ensemble of colour nitrogen-vacancy centres in diamond and the superconducting flux-qubit. We also design a Carnot cycle that traverses Exceptional Points in the broken symmetry phase for temperatures above the critical value, achieving the same efficiency as the classical Carnot cycle. Furthermore, we implement a Stirling cycle whose efficiency surpasses its classical counterpart, particularly when operating near Exceptional Points. Finally, we outline how the model can be scaled to larger Hilbert-space dimensions.

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arXiv2025

Non-standard quantum algebras and infinite-dimensional PT-symmetric systems

In this work, we introduce a PT-symmetric infinite-dimensional representation of the Uz(sl(2,R)) Hopf algebra, and we analyse a multiparametric family of Hamiltonians constructed from such representation of the generators of this non-standard quantum algebra. It is shown that all these Hamiltonians can be mapped to equivalent systems endowed with a position-dependent mass. From the latter presentation, it is shown how appropriate point canonical transformations can be further defined in order to transform them into Hamiltonians with constant mass over suitable domains. By following this approach, the bound-state spectrum and the corresponding eigenfunctions of the initial PT-symmetric Hamiltonians can be determined. It is worth stressing that a relevant feature of some of the new Uz(sl(2,R)) systems here presented is found to be their connection with double-well and Pöschl-Teller potentials. In fact, as an application we present a particular Hamiltonian that can be expressed as an effective double-well trigonometric potential, which is commonly used to model several relevant systems in molecular physics.

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arXiv2024

Complex Scaling Method applied to the study of the Swanson Hamiltonian in the broken PT-symmetry phase

In this work, we study the non-PT symmetry phase of the Swanson Hamiltonian in the framework of the Complex Scaling Method. By constructing a bi-orthogonality relation, we apply the formalism of the response function to analyse the time evolution of different initial wave packages. The Wigner Functions and mean value of operators are evaluated as a function of time. We analyse in detail the time evolution in the neighbourhood of Exceptional Points. We derive a continuity equation for the system. We compare the results obtained using the Complex Scaling Method to the ones obtained by working in a Rigged Hilbert Space.

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arXiv2024

Phase transitions and thermodynamic cycles in the broken PT-regime

We propose a new type of quantum thermodynamic cycle whose efficiency is greater than the one of the classical Carnot cycle for the same conditions for a system when viewed as homogeneous. In our model this type of cycle only exists in the low temperature regime in the spontaneously broken parity-time-reversal (PT) symmetry regime of a non-Hermitian quantum theory and does not manifest in the PT-symmetric regime. We discuss this effect for an ensemble based on a model of a single boson coupled in a non-Hermitian way to a bath of different types of bosons with and without a time-dependent boundary. The cycle can not be set up when considering our system as heterogeneous, i.e. undergoing a first order phase transition. Within that interpretation we find that the entropy is vanishing throughout the spontaneously broken PT-regime.

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arXiv2023

Non-standard quantum algebras and finite dimensional $\mathcal{PT}$-symmetric systems

In this work, $\mathcal{PT}$-symmetric Hamiltonians defined on quantum $sl(2, \mathbb R)$ algebras are presented. We study the spectrum of a family of non-Hermitian Hamiltonians written in terms of the generators of the non-standard $U_{z}(sl(2, \mathbb R))$ Hopf algebra deformation of $sl(2, \mathbb R)$. By making use of a particular boson representation of the generators of $U_{z}(sl(2, \mathbb R))$, both the co-product and the commutation relations of the quantum algebra are shown to be invariant under the $\mathcal{PT}$-transformation. In terms of these operators, we construct several finite dimensional $\mathcal{PT}$-symmetry Hamiltonians, whose spectrum is analytically obtained for any arbitrary dimension. In particular, we show the appearance of Exceptional Points in the space of model parameters and we discuss the behaviour of the spectrum both in the exact $\mathcal{PT}$-symmetry and the broken $\mathcal{PT}$-symmetry dynamical phases. As an application, we show that this non-standard quantum algebra can be used to define an effective model Hamiltonian describing accurately the experimental spectra of three-electron hybrid qubits based on asymmetric double quantum dots. Remarkably enough, in this effective model, the deformation parameter $z$ has to be identified with the detuning parameter of the system.

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arXiv2022

Psedo-hermitian Hamiltonians at finite temperature

The Double Green Function Formalism has been extensively used in dealing with the thermodynamics of quantum systems which evolved in time under the action of a given self-adjoint Hamiltonian. In this work, we extend the formalism to include pseudo-hermitian Hamiltonians. We apply the formalism to study the PT-symmetry Swanson Hamiltonian at finite temperature, both in the PT-unbroken and in the PT-broken symmetry phase. We analyse the behaviour of the system, which is initially at equilibrium at a given temperature, when it is perturbed by a periodic interaction.

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arXiv2020

Excepional Points from Hamiltonians of hybrid physical systems: Squeezing and anti-Squeezing

We study the appearance of Exceptional Points in a hybrid system composed of a superconducting flux-qubit and an ensemble of nitrogen-vacancy colour centres in diamond. We discuss the possibility of controlling the generation of Exceptional Points, by the analysis of the model space parameters. One of the characteristic features of the presence of Exceptional Points, it is the departure from the exponential decay behaviour of the observables as a function of time. We study the time evolution of different initial states, in the presence of the hybrid system, by computing the reduced density matrix of each subsystem. We present the results we have obtained for the steady behaviour of different observables. We analyse the appearance of Squeezed Spin States and of anti-Squeezed Spin States.

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arXiv2007

Effective su_q(2) models and polynomial algebras for fermion-boson Hamiltonians

Schematic su(2)+h3 interaction Hamiltonians, where su(2) plays the role of the pseudo-spin algebra of fermion operators and h3 is the Heisenberg algebra for bosons, are shown to be closely related to certain nonlinear models defined on a single quantum algebra q-su(2) of quasifermions. In particular, q-su(2) analogues of the Da Providencia-Schutte and extended Lipkin models are presented. The connection between q and the physical parameters of the fermion-boson system is analysed, and the integrability properties of the interaction Hamiltonians are discussed by using polynomial algebras.

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