arXiv subjects

Tomáš Novotný

Publications and source records attributed to Tomáš Novotný.

At least 19 recordsLinked to original sources

arXiv2026

Robust Graph Isomorphism, Quadratic Assignment and VC Dimension

We present an additive $\varepsilon n^{2}$-approximation algorithm for the Graph Edit Distance problem (GED) on graphs of VC dimension $d$ running in time $n^{O(d/\varepsilon^{2})}$. In particular, this recovers a previous result by Arora, Frieze, and Kaplan [Math. Program. 2002] who gave an $\varepsilon n^{2}$-approximation running in time $n^{O(\log n/\varepsilon^{2})}$. Similar to the work of Arora et al., we extend our results to arbitrary Quadratic Assignment problems (QAPs) by introducing a notion of VC dimension for QAP instances, and giving an $\varepsilon n^{2}$-approximation for QAPs with bounded weights running in time $n^{O(\varepsilon^{-2}(d + \log\varepsilon^{-1}))}$. As a particularly interesting special case, we further study the problem $\varepsilon$-$\mathsf{GI}$, which entails determining if two graphs $G,H$ over $n$ vertices are isomorphic, when promised that if they are not, their graph edit distance is at least $\varepsilon n^{2}$. We show that the standard Weisfeiler--Leman algorithm of dimension $O(\varepsilon^{-1}d\log(\varepsilon^{-1}))$ solves this problem on graphs of VC dimension $d$. We also show that dimension $O(\varepsilon^{-1}\log n)$ suffices on arbitrary $n$-vertex graphs, while $k$-WL fails on instances at distance $Ω(n^{2}/k)$.

cs.DS↗

arXiv2025

Universal Scaling of Electron Transmission for Nearly Ballistic and Quantum Dragon Nanodevices

We predict two different universal scaling regimes for the quantum transmission of metallic nanodevices following the addition of a small amount of uncorrelated disorder. A nanodevice is connected to two thin semi-infinite uniform leads, and the Non-Equilibrium Green's Function (NEGF) methodology yields the electron transmission ${\cal T}(E)$ as a function of the injected electron energy $E$. Ballistic nanodevices have no disorder and have ${\cal T}(E)=1$ for all $E$ that allow electron propagation in the leads. Quantum dragon nanodevices can have extremely strong properly correlated disorder, and still have ${\cal T}(E)=1$ for all $E$. Additional uncorrelated site disorder leads to Fano resonances in ${\cal T}(E)$. Averaging over the uncorrelated disorder we predict using perturbation theory two universal scaling regimes for ${\cal T}_{\rm ave}(E)$. The functional form of both universal scaling regimes depend on the device length and width, energy, and variance of the uncorrelated disorder. The second scaling regime, valid for small but somewhat larger uncorrelated disorder than the first scaling regime, also has the form dependent on the density of states of the system. These two scaling regimes are demonstrated to be valid via large scale computer calculations.

cond-mat.mes-hall↗

arXiv2025

Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models

This work systematically investigates the phase diagram of a parallel double-quantum-dot Andreev molecule, where the two quantum dots are coupled to a common superconducting lead. Using the numerical renormalization group method, we map out the evolution of the ground state across a wide parameter space of level detunings, size of the superconducting gap, lead couplings, and inter-dot coupling strength. The intricate phase diagrams feature singlet, doublet, and a relatively uncommon triplet ground states, with the latter being a distinct signature of strong lead-mediated interactions between the quantum dots. We benchmark the applicability of simplified effective models, including the atomic limit and zero-bandwidth approximations, in capturing the complex behavior of this parallel configuration. Our analysis reveals severe limitations of these models, underscoring the necessity for maximal caution when extrapolating beyond their tested validity. In particular, all effective models except for the extended version of the zero-bandwidth approximation failed in reproducing the triplet ground state and made several false predictions. These findings provide crucial insights for interpreting experimental observations and designing superconducting devices based on quantum-dot architectures.

cond-mat.mes-hall↗

arXiv2025

High harmonic generation in monolayer MoS2 controlled by resonant and near-resonant pulses on ultrashort time scales

We report on experimental investigation of nonperturbative high harmonic generation (HHG) in monolayer MoS2 in the ultraviolet spectral region driven by mid-infrared light. We study how the HHG is influenced by pre-excitation of the monolayer using resonant and near-resonant pulses in a pump-probe-like scheme. The resonant light creates high density exciton population. Due to ultrafast dephasing caused by electron-electron scattering, the HHG is suppressed in the presence of pre-excited carriers. In the case of near-resonant excitation with photon energy below the exciton transition, the dynamics of the observed suppression of the HHG yield contains a fast component which is a consequence of momentum scattering at carriers, which are excited by two-photon transition when the two pulses temporally overlap in the sample. This interpretation is supported by comparison of the experimental data with theoretical calculations of two-photon absorption spectrum of MoS2 monolayer. This work demonstrates a possibility to control HHG in lowdimensional materials on ultrashort timescales by combining the driving strong-field pulse with a weak near-resonant light.

physics.optics↗

arXiv2025

Monochromatization of Electron Beams with Spatially and Temporally Modulated Optical Fields

Inelastic interaction between coherent light with constant frequency and free electrons enables periodic phase modulation of electron wave packets leading to periodic side-bands in the electron energy spectra. In this Letter we propose a generalization of the interaction by considering linearly chirped electron wave packets interacting with chirped optical fields. We theoretically demonstrate that when matching the chirp parameters of the electron and light waves, the interaction leads to partial monochromatization of the electron spectra in one of the energy side-bands. Depending on the coherence time of the electrons, the electron spectrum may be narrowed down by a factor of 5-times with 26% of the electron distribution in the monochromatized energy band. This approach will improve the spectral resolution and reduce color aberrations in ultrafast imaging experiments with free electrons.

physics.optics↗

arXiv2024

Fractional positional jumps in stochastic systems with tilted periodic double-well potentials

We present a theoretical investigation of the stochastic dynamics of a damped particle in a tilted periodic potential with a double well per period. By applying the matrix continued fraction technique to the Fokker-Planck equation in conjunction with the full counting statistics and master equation approaches, we determine the rates of specific processes contributing to the system's overall dynamics. At low temperatures, the system can exhibit one running state and two distinct locked metastable states. We focus primarily on two aspects: the dynamics of positional jumps, which are rare thermally induced particle jumps over potential maxima, and their impact on the overall velocity noise; and the retrapping process, involving the transition from the running to the locked metastable states. We demonstrate the existence of fractional (in units of $2π$) positional slips that differ qualitatively from conventional $2π$ jumps observed in single-well systems. Fractional positional slips significantly influence the system dynamics even in regimes dominated by dichotomous-like switching between running and locked states. Furthermore, we introduce a simple master equation approach that proves effective in analyzing various stages of the retrapping process. Interestingly, our analysis shows that even for a system featuring a well-developed double-well periodic potential, there exists a broad parameter range where the stochastic dynamics can be accurately described by an effective single-well periodic model. The techniques introduced here allow for valuable insights into the complex behavior of the system, offering avenues for understanding and controlling its steady-state and transient dynamics, which go beyond or can be complementary to direct stochastic simulations.

cond-mat.stat-mech↗

arXiv2024

Synthesizing and multiplexing autonomous quantum coherences

Quantum coherence is a crucial prerequisite for quantum technologies. Therefore, the robust generation, as autonomous as possible, of quantum coherence remains the essential problem for developing this field. We consider a method of synthesizing and multiplexing quantum coherence from spin systems without any direct drives only coupled to bosonic baths. The previous studies in this field have demonstrated that a back-action of the bath to the spin subsystem is important to generate it, however, it simultaneously gives significant limits to the generated coherence. We propose a viable approach with the bosonic bath that allows overcoming these limits by avoiding the destructive effect of the back-action processes. Using this approach, we suggest an advanced synthesis of the quantum coherence non-perturbatively in the spin-boson coupling parameters of multiple bosonic baths to increase and multiplex it for upcoming proof-of-principle experiments.

quant-ph↗

arXiv2023

Generalized atomic limit of a double quantum dot coupled to superconducting leads

We present an exactly solvable effective model of a double quantum dot coupled to superconducting leads. This model is a generalization of the well-known superconducting atomic limit approximation of the paradigmatic superconducting impurity Anderson model. However, in contrast to the standard atomic limit and other effective models, it gives quantitatively correct predictions for the quantum phase transition boundaries, subgap bound states as well as Josephson supercurrent in a broad range of parameters including experimentally relevant regimes. The model allows fast and reliable parameter scans important for the preparation and analysis of experiments which are otherwise inaccessible by more precise but computational heavy methods such as quantum Monte Carlo or the numerical renormalization group. The scans also allowed us to identify and investigate new previously unnoticed phase diagram regimes. We provide a thorough analysis of the strengths and limitations of the effective model and benchmark its predictions against numerical renormalization group results.

cond-mat.mes-hall↗

arXiv2022

Phase diffusion and noise temperature of a microwave amplifier based on single unshunted Josephson junction

High-gain microwave amplifiers operating near quantum limit are crucial for development of quantum technology. However, a systematic theoretical modeling and simulations of their performance represent rather challenging tasks due to the occurrence of colored noises and nonlinearities in the underlying circuits. Here, we develop a response theory for such an amplifier whose circuit dynamics is based on nonlinear oscillations of an unshunted Josephson junction. The theory accounts for a subtle interplay between exponentially damped fluctuations around the stable limit cycle and the nonlinear dynamics of the limit cycle phase. The amplifier gain and noise spectrum are derived assuming a colored voltage noise at the circuit resistor. The derived expressions are generally applicable to any system whose limit cycle dynamics is perturbed by a colored noise and a harmonic signal. We also critically assess reliabilities of numerical methods of simulations of the corresponding nonlinear Langevin equations, where even reliable discretization schemes might introduce errors significantly affecting simulated characteristics at the peak performance.

cond-mat.stat-mech↗

arXiv2022

Extraction of autonomous quantum coherences

Quantum coherence is an essential resource to gain advantage over classical physics and technology. Recently, it has been proposed that a low-temperature environment can induce quantum coherence of a spin without an external coherent pump. We address a critical question if such coherence is extractable by a weak coupling to an output system dynamically affecting back the spin-environment coupling. Describing the entire mechanism, we prove that such extraction is generically possible for output spins (also oscillators or fields) and, as well, in a fermionic analogue of such a process. We compare the internal spin coherence and output coherence over temperature and characteristic frequencies. The proposed optimal coherence extraction opens paths for the upcoming experimental tests with atomic and solid-state systems.

quant-ph↗

arXiv2021

Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads

We derive and apply a general scheme for mapping a setup consisting of a half-filled single level quantum dot coupled to one normal metallic and two superconducting phase-biased leads onto an ordinary half-filled single impurity Anderson model with single modified tunneling density of states. The theory allows for the otherwise unfeasible application of the standard numerical renormalization group and enables to obtain phase-dependent local spectral properties as well as phase-dependent induced pairing and Josephson current. The resulting transport properties match well with the numerically exact continuous-time hybridization-expansion quantum Monte Carlo. For weakly coupled normal electrode, the spectral properties can be interpreted in terms of normal-electrode-broadened Andreev bound states with phase-dependent position analogous to the superconducting Anderson model, which coexist in the $π$-like phase with a Kondo peak whose phase-dependent Kondo temperature follows the form conjectured previously in Domański et al., Phys.~Rev.~B {\bf 95}, 045104 (2017)

cond-mat.mes-hall↗

arXiv2021

Resolving Ambiguity of the Kondo Temperature Determination in Mechanically Tunable Single-Molecule Kondo Systems

Determination of the molecular Kondo temperature $T_K$ poses a challenge in most cases when the experimental temperature cannot be tuned to a sufficient extent. We show how this ambiguity can be resolved if additional control parameters are present, such as magnetic field and mechanical gating. We record the evolution of the differential conductance by lifting an individual molecule from the metal surface with the tip of a scanning tunneling microscope. By fitting the measured conductance spectra with the single impurity Anderson model we are able to demonstrate that the lifting tunes the junction continuously from the strongly correlated Kondo-singlet to the free spin $1/2$ ground state. In the crossover regime, where $T_K$ is similar to the temperature of experiment, the fitting yields ambiguous estimates of $T_K$ varying by an order of magnitude. We show that analysis of the conductance measured in two distinct external magnetic fields can be used to resolve this problem.

cond-mat.mes-hall↗

arXiv2021

Tunable reentrant Kondo effect in quantum dots coupled to metal-superconducting hybrid reservoirs

We elaborate on the recently introduced concept of reentrant Kondo effect in quantum impurities/dots coupled to hybrid metal-semiconductor contacts [G.~Diniz {\em et al.}, Phys. Rev. B {\bf 101}, 125115 (2020)]. By noticing the equivalence of the originally suggested semiconducting arrangement to an analogous three-terminal quantum dot setup with a normal and two phase-biased superconducting leads introduced in our recent work [Phys. Rev. B {\bf 103}, 035419 (2021)], we put this effect into a new physical context, which enables us a fresh look on the problem. First, we identify the superconducting counterpart of the reentrant Kondo effect and, consequently, reveal its fragility with respect to an underlying doublet-singlet quantum phase transition induced by the particle-hole asymmetry of the reservoir densities of states. This is pertinent (even if previously unnoticed) also in the original as well as extended semiconducting setups, where it puts stringent conditions on the symmetry of the contact density of states. Furthermore, we analyze experimental feasibility of observing the reentrant Kondo effect in its superconducting realization concluding that even present day experiments might see the onset of the reentrant behavior, but fully developed Kondo features cannot be reached due to the required vast separation of energy/temperature scales.

cond-mat.mes-hall↗

arXiv2021

Footprints of impurity quantum phase transitions in quantum Monte Carlo statistics

Interacting single-level quantum dot connected to BCS superconducting leads represents a well-controllable system to study the interplay between the correlation effects and the electron pairing that can result in a $0-π$ (singlet-doublet) quantum phase transition. The physics of this system can be well described by the impurity Anderson model. We present an analysis of the statistics of the perturbation expansion order of the continuous-time hybridization expansion quantum Monte Carlo algorithm in the vicinity of such a first-order impurity quantum phase transition. By calculating the moments of the histograms of the expansion order which deviate from the ideal Gaussian shape, we provide an insight into the thermodynamic mixing of the two phases at low but finite temperatures which is reflected in the bimodal nature of the histograms.

cond-mat.mes-hall↗

arXiv2020

Effects of noise-induced coherence on the fluctuations of current in quantum absorption refrigerators

We investigate the effects of noise-induced coherence on average current and current fluctuations in a simple model of quantum absorption refrigerator with degenerate energy levels. We describe and explain the differences and similarities between the system behavior when it operates in the classical regime, where the populations and coherences in the corresponding quantum optical master equation decouple in a suitably chosen basis, and in the quantum regime, where such a transformation does not exist. The differences between the quantum and the classical case are observable only close to the maximum current regime, where the system steady-state becomes non-unique. This allows us to approximate the system dynamics by an analytical model based on a dichotomous process, that explains the behavior of the average current both in the classical and in the quantum case. Due to the non-uniqueness, the scaled cumulant generating function for the current at the vicinity of the critical point exhibits behavior reminiscent of the dynamical first-order phase transition. Unless the system parameters are fine-tuned to a single point in the parameter space, the corresponding current fluctuations are moderate in the quantum case and large in the classical case.

cond-mat.stat-mech↗

arXiv2020

Practical Guide to Quantum Phase Transitions in Quantum-Dot-Based Tunable Josephson Junctions

Quantum dots attached to BCS superconducting leads exhibit a $0-π$ impurity quantum phase transition, which can be experimentally controlled either by the gate voltage or by the superconducting phase difference. For the pertinent superconducting single-impurity Anderson model, we newly present two simple analytical formulae describing the position of the phase boundary in parameter space for the weakly correlated and Kondo regime, respectively. Furthermore, we show that the two-level approximation provides an excellent description of the low temperature physics of superconducting quantum dots near the phase transition. We discuss reliability and mutual agreement of available finite temperature numerical methods (Numerical Renormalization Group and Quantum Monte Carlo) and suggest a novel approach for efficient determination of the quantum phase boundary from measured finite temperature data. Our results enable fast and efficient, yet reliable characterization and design of such nanoscopic tunable Josephson junction devices.

cond-mat.mes-hall↗

arXiv2020

Magnetically-Tuned Kondo Effect in a Molecular Double Quantum Dot: Role of the Anisotropic Exchange

We investigate theoretically and experimentally the singlet-triplet Kondo effect induced by a magnetic field in a molecular junction. Temperature dependent conductance, $G(T)$, is calculated by the numerical renormalization group, showing a strong imprint of the relevant low energy scales, such as the Kondo temperature, exchange and singlet-triplet splitting. We demonstrate the stability of the singlet-triplet Kondo effect against weak spin anisotropy, modeled by an anisotropic exchange. Moderate spin anisotropy manifests itself by lowering the Kondo plateaus, causing the $G(T)$ to deviate from a standard temperature dependence, expected for a spin-half Kondo effect. We propose this scenario as an explanation for anomalous $G(T)$, measured in an organic diradical molecule coupled to gold contacts. We uncover certain new aspects of the singlet-triplet Kondo effect, such as coexistence of spin-polarization on the molecule with Kondo screening and non-perturbative parametric dependence of an effective magnetic field induced by the leads.

cond-mat.mes-hall↗

arXiv2019

Second Order Perturbation Theory for a Superconducting Double Quantum Dot

We extend our approach based on the second order perturbation theory in the Coulomb interaction recently developed for quantum dots coupled to superconducting leads to the superconducting double quantum dot setups. Using our perturbative method we evaluate several single-particle quantities such as on-dot induced gap and generalized occupations together with the Andreev in-gap spectra and compare them with numerically exact results from the Numerical Renormalization Group and Quantum Monte Carlo finding a very good correspondence for not too strongly correlated regimes. Thus we can offer in a wide parameter range this method as an efficient and reliable alternative to the heavy numerical tools exclusively used so far for the description of such experimentally relevant systems.

cond-mat.mes-hall↗