Opening the system to the environment: new theories and tools in classical and quantum settings

The thesis is organized as follows. Section 2 is a first, unconventional, approach to the topic of EPs. Having grown interest in the topic of combinatorics and graph theory, I wanted to exploit its very abstract and mathematical tools to reinterpret something very physical, that is, the EPs in wave scattering. To do this, I build the interpretation of scattering events from a graph theory perspective and show how EPs can be understood within this interpretation. In Section 3, I move from a completely classical treatment to a purely quantum one. In this section, I consider two quantum resonators coupled to two baths and study their dynamics with local and global master equations. Here, the EPs are the key physical features used as a witness of validity of the master equation. Choosing the wrong master equation in the regime of interest can indeed mask physical and fundamental features of the system. In Section 4, there are no EPs. However I transition towards a classical/quantum framework via the topic of open systems. My main contribution in this work is the classical stochastic treatment and simulation of a spin coupled to a bath. In this work, I show how a natural quantum--to--classical transition occurs at all coupling strengths when certain limits of spin length are taken. As a key result, I also show how the coupling to the environment in this stochastic framework induces a classical counterpart to quantum coherences in equilibrium. After this last topic, in Section 5, I briefly present the key features of the code I built (and later extended) for the latter project. This, in the form of a Julia registry package named SpiDy.jl, has seen further applications in branching projects and allows for further exploration of the theoretical framework. Finally, I conclude with a discussion section (see Sec. 5) where I recap the different conclusions gathered in the previous sections and propose several possible directions.Engineering and Physical Sciences Research Council (EPSRC

Parental species and hybrid descendants of Bacillus (Insecta Phasmatodea) show different patterns of highly amplified, colocalized ribosomal and telomeric sequences

We investigated by dual-color fluorescence in situ hybridization (FISH) with 28S ribosomal and (TTAGG)n telomeric probes all species of the circum-Mediterranean genus Bacillus encompassing bisexual and parthenogenetic taxa, namely the three parental species (B. grandii, B. atticus, B. rossius) and the two derived hybrids (B. whitei, B. lynceorum). Specimens were collected in Italian mainland, Sardinia and Sicily. In all species the presence of colocalized, highly amplified ribosomal and telomeric sequences was demonstrated by the double labelling of the cytological satellites. These satellites varied in size, number and location both among and within species. In B. grandii and B. atticus a maximum of two FISH-labeled locations were observed, whereas in B. rossius and in the two hybrids up to 11 different positions were recorded. Moreover, our investigations showed a significant occurrence of chromosome breakages and rearrangements. The overall meaning of the ribosomal and telomeric sequence colocalization as well as the Nucleolar Organizer Region mobility and activity are discussed in both the ancestors and their hybrid descendants. It is noteworthy that the same trait has been shown in seven additional phasmid species belonging to distantly related genera. This trait could be a shared ancestral character in phasmids

Entanglement distance for arbitrary M -qudit hybrid systems

This is the final version. Available from the American Physical Society via the DOI in this recordThe achievement of quantum supremacy boosted the need for a robust medium of quantum information. In this task, higher-dimensional qudits show remarkable noise tolerance and enhanced security for quantum key distribution applications. However, to exploit the advantages of such states, we need a thorough characterisation of their entanglement. Here, we propose a measure of entanglement which can be computed either for pure and mixed states of a $M$-qudit hybrid system. The entanglement measure is based on a distance deriving from an adapted application of the Fubini-Study metric. This measure is invariant under local unitary transformations and has an explicit computable expression that we derive. In the specific case of $M$-qubit systems, the measure assumes the physical interpretation of an obstacle to the minimum distance between infinitesimally close states. Finally, we quantify the robustness of entanglement of a state through the eigenvalues analysis of the metric tensor associated with it.QuantERA ERA-NET Co-fundEngineering and Physical Sciences Research Council (EPSRC

Quantum–classical correspondence in spin–boson equilibrium states at arbitrary coupling

The equilibrium properties of nanoscale systems can deviate significantly from standard thermodynamics due to their coupling to an environment. We investigate this here for the θ-angled spin–boson model, where we first derive a compact and general form of the classical equilibrium state including environmental corrections to all orders. Secondly, for the quantum spin–boson model we prove, by carefully taking a large spin limit, that Bohr’s quantum–classical correspondence persists at all coupling strengths. This shows, for the first time, the validity of the quantum–classical correspondence for an open system and gives insight into the regimes where the quantum system is well-approximated by a classical one. Finally, we provide the first classification of the coupling parameter regimes for the spin–boson model, from weak to ultrastrong, both for the quantum case and the classical setting. Our results shed light on the interplay of quantum and mean force corrections in equilibrium states of the spin–boson model, and will help draw the quantum to classical boundary in a range of fields, such as magnetism and exciton dynamics

The topology of data hides in quantum thermal states

This is the final version. Available on open access from AIP Publishing via the DOI in this record Data availability: The data that support the findings of this study are available within the article.We provide a quantum protocol to perform topological data analysis (TDA) via the distillation of quantum thermal states. Recent developments in quantum thermal state preparation algorithms reveal their characteristic scaling, defined by the properties of dissipative Lindbladians. This contrasts with protocols based on unitary evolution, which have a scaling depending on the properties of the combinatorial Laplacian. To leverage quantum thermal state preparation algorithms, we translate quantum TDA from a real-time to an imaginary-time picture, shifting the paradigm from a unitary approach to a dissipative one. Starting from an initial state overlapping with the ground state of the system, one can dissipate its energy via channels unique to the dataset, naturally distilling its information. Therefore, calculating Betti numbers translates into a purity estimation. Alternatively, this can be interpreted as the evaluation of the Rényi two-entropy, Uhlmann fidelity, or Hilbert–Schmidt distance relative to thermal states with the embedded topology of simplicial complexes. Our work opens the field of TDA toward a more physical interpretation of the topology of data.Innovate U

Local master equations bypass the secular approximation

This is the author accepted manuscript. The final version is available on open access from Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften via the DOI in this recordMaster equations are a vital tool to model heat flow through nanoscale thermodynamic systems. Most practical devices are made up of interacting sub-system, and are often modelled using either local master equations (LMEs) or global master equations (GMEs). While the limiting cases in which either the LME or the GME breaks down are well understood, there exists a 'grey area' in which both equations capture steady-state heat currents reliably, but predict very different transient heat flows. In such cases, which one should we trust? Here, we show that, when it comes to dynamics, the local approach can be more reliable than the global one for weakly interacting open quantum systems. This is due to the fact that the secular approximation, which underpins the GME, can destroy key dynamical features. To illustrate this, we consider a minimal transport setup and show that its LME displays exceptional points (EPs). These singularities have been observed in a superconducting-circuit realisation of the model [1]. However, in stark contrast to experimental evidence, no EPs appear within the global approach. We then show that the EPs are a feature built into the Redfield equation, which is more accurate than the LME and the GME. Finally, we show that the local approach emerges as the weak-interaction limit of the Redfield equation, and that it entirely avoids the secular approximation.Engineering and Physical Sciences Research Council (EPSRC)Royal Societ

Mirrored images but not silicone models trigger aggressive responses in male common wall lizards

Disentangling the effects of single releasers in animal communication is a demanding task because a releaser often consists of a combination of different key stimuli. Territorial communication in reptiles usually depends on visual, chemical, and acoustic stimuli, but the role of each of them depends on phylogeny. Lacertids are modern lizards that rely mainly on chemical cues for their communication, but they also use aggressive displays based on visual recognition. We experimentally tested the visual stimuli that release an aggressive response in the males of a typical lacertid, the common wall lizard (Podarcis muralis), testing the effects of silicone models and mirrored images in captivity. The response to models and control (a blank sheet) was not significantly different and these stimuli did not release any aggressive behaviour. On the contrary, the reflected image in a mirror caused overt aggression (i.e., bites against it) in 63% of tested individuals. The results clearly demonstrate the role of visual stimuli in territorial communication, but only as a combined effect of shape and motion, differently from other lizard families for which shape is enough to stimulate aggre sive responses. Mirrors can be useful tools to investigate aggression related to physiological and morphological aspects in lacertid lizards

Fate of patients with spinal cord ischemia complicating thoracic endovascular aortic repair

ObjectiveSpinal cord ischemia (SCI) is a potentially devastating complication of thoracic endovascular aortic repair (TEVAR) that can result in varying degrees of short-term and permanent disability. This study was undertaken to describe the clinical outcomes, long-term functional impact, and influence on survival of SCI after TEVAR.MethodsA retrospective review of all TEVAR patients at the University of Florida from 2000 to 2011 was performed to identify individuals experiencing SCI, defined by any new lower extremity neurologic deficit not attributable to another cause. SCI was dichotomized into immediate or delayed onset, with immediate onset defined as SCI noted upon awakening from anesthesia, and delayed characterized as a period of normal function, followed by development of neurologic injury. Ambulatory status was determined using database query, record review, and phone interviews with patients and/or family. Mortality was estimated using life-table analysis.ResultsA total of 607 TEVARs were performed for various indications, with 57 patients (9.4%) noted to have postoperative SCI (4.3% permanent). SCI patients were more likely to be older (63.9 ± 15.6 vs 70.5 ± 11.2 years; P = .002) and have a number of comorbidities, including chronic obstructive pulmonary disease, hypertension, dyslipidemia, and cerebrovascular disease (P < .0001). At some point in their care, a cerebrospinal fluid drain was placed in 54 patients (95%), with 54% placed postoperatively. In-hospital mortality was 8.8% for the entire cohort (SCI vs no SCI; P = .45). SCI developed immediately in 12 patients, delayed onset in 40, and indeterminate in five patients due to indiscriminate timing from postoperative sedation. Three patients (25%) with immediate SCI had measurable functional improvement (FI), whereas 28 (70%) of the delayed-onset patients experienced some degree of neurologic recovery (P = .04). Of the 34 patients with complete data available, 26 (76%) reported quantifiable FI, but only 13 (38%) experienced return to their preoperative baseline. Estimated mean (± standard error) survival for patients with and without SCI was 37.2 ± 4.5 and 71.6 ± 3.9 months (P < .0006), respectively. Patients with FI had a mean survival of 53.9 ± 5.9 months compared with 9.6 ± 3.6 months for those without improvement (P < .0001). Survival and return of neurologic function were not significantly different when patients with preoperative and postoperative cerebrospinal fluid drains were compared.ConclusionsThe minority of patients experience complete return to baseline function after SCI with TEVAR, and outcomes in patients without early functional recovery are particularly dismal. Patients experiencing delayed SCI are more likely to have FI and may anticipate similar life-expectancy with neurologic recovery compared with patients without SCI. Timing of drain placement does not appear to have an impact on postdischarge FI or long-term mortality