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Bijay Kumar Agarwalla

Publications and source records attributed to Bijay Kumar Agarwalla.

At least 37 records · Page 2Linked to original sources
arXiv2025

Quantum trajectories and Page-curve entanglement dynamics

We consider time dynamics of entanglement entropy between a filled fermionic system and an empty reservoir. We consider scenarios (i) where the system is subjected to a dephasing mechanism and the reservoir is clean, thereby emulating expansion of effectively interacting fermions in vacuum, and (ii) where both the system and the reservoir are subjected to dephasing and thereby enabling us to address how the entanglement between the part of the effectively interacting system and its complement evolves in time. We consider two different kinds of quantum trajectory approaches, namely stochastic unitary unraveling and quantum state diffusion. For both protocols, we observe and characterize the full Page curve-like dynamics for the entanglement entropy. Depending on the protocol and the setup, we observe very distinct characteristics of the Page curve and the associated Page time and Page value. We also compute the number of fermions leaking to the reservoir and the associated current and shed light on their plausible connections with entanglement entropy. Our findings are expected to hold for a wide variety of generic interacting quantum systems.

cond-mat.stat-mech↗
arXiv2024

Collective Dissipation of Oscillator Dipoles Strongly Coupled to 1-D Electromagnetic Reservoirs

We study the collective dissipative dynamics of dipoles modeled as harmonic oscillators coupled to 1-D electromagnetic reservoirs. The bosonic nature of the dipole oscillators as well as the reservoir modes allows an exact numerical simulation of the dynamics for arbitrary coupling strengths. At weak coupling, apart from essentially recovering the dynamics expected from a Markovian Lindblad master equation, we also obtain non-Markovian effects for spatially separated two-level emitters. In the so called ultrastrong coupling regime, we find the dynamics and steady state depends on the choice of the reservoir which is chosen as either an ideal cavity with equispaced, unbounded dispersion or a cavity array with a bounded dispersion. Moreover, at even higher coupling strengths, we find a decoupling between the light and matter degrees of freedom attributable to the increased importance of the diamagnetic term in the Hamiltonian. In this regime, we find that the dependence of the dynamics on the separation between the dipoles is not important and the dynamics is dominated by the occupation of the polariton mode of lowest energy.

quant-ph↗
arXiv2024

Higher-order gap ratios of singular values in open quantum systems

Understanding open quantum systems using information encoded in its complex eigenvalues has been a subject of growing interest. In this paper, we study higher-order gap ratios of the singular values of generic open quantum systems. We show that $k$-th order gap ratio of the singular values of an open quantum system can be connected to the nearest-neighbor spacing ratio of positions of classical particles of a harmonically confined log-gas with inverse temperature $β'(k)$ where $β'(k)$ is an analytical function that depends on $k$ and the Dyson's index $β=1,2,$ and $4$ that characterizes the properties of the associated Hermitized matrix. Our findings are crucial not only for understanding long-range correlations between the eigenvalues but also provide an excellent way of distinguishing different symmetry classes in an open quantum system. To highlight the universality of our findings, we demonstrate the higher-order gap ratios using different platforms such as non-Hermitian random matrices, random dissipative Liouvillians, Hamiltonians coupled to a Markovian bath, and Hamiltonians with in-built non-Hermiticity.

cond-mat.stat-mech↗
arXiv2024

Transport in open quantum systems in presence of lossy channels

We study nonequilibrium steady state (NESS) transport in a boundary driven one-dimensional fermionic lattice setup which is further subjected to particle loss. We analyze the system size scaling of conductance at zero temperature for different values of the chemical potential of the boundary reservoirs. We consider a variety of loss channel configurations: (i) single loss at the middle site of the lattice, (ii) multiple but nonextensive lossy channels, and (iii) extensive lossy channels. For the cases (i) and (ii), the conductance scaling with system size remains robust (i.e., same as the case with no loss) for chemical potential within and outside the lattice band, while at the band-edge rich anomalous conductance scaling emerges. For case (iii), the conductance scaling becomes ballistic in the thermodynamic limit for any value of chemical potential. We explain the emergence of these different system size scalings of conductance by analyzing the spectral properties of the associated non-hermitian transfer matrices of the underlying lattice. We demonstrate that the emergence of anomalous scaling is deeply connected to the existence of exceptional points of transfer matrices. Our study unravels that by carefully optimizing the loss mechanism configurations, one can in principle realize systems with rich transport properties in low-dimensional open quantum systems.

cond-mat.stat-mech↗
arXiv2024

Arbitrary order transfer matrix exceptional points and van Hove singularities

In lattice models with quadratic finite-range Hermitian Hamiltonians, the inherently non-Hermitian transfer matrix (TM) governs the band dispersion. The van Hove singularities (VHSs) are special points in the band dispersion where the density of states (DOS) diverge. Considering a lattice chain with hopping of a finite range $n$, we find a direct fundamental connection between VHSs and exceptional points (EPs) of TM, both of arbitrary order. In particular, we show that VHSs are EPs of TM of the same order, thereby connecting two different types of critical points usually studied in widely different branches of physics. Consequently, several properties of band dispersion and VHSs can be analyzed in terms of spectral properties of TM. We further provide a general prescription to generate any order EP of the TM and therefore corresponding VHS. For a given range of hopping $n$, our analysis provides restrictions on allowed orders of EPs of TM. Finally, we exemplify all our results for the case $n=3$.

quant-ph↗
arXiv2024

Effect of order of transfer matrix exceptional points on transport at band edges

Recently, it has been shown that, in one dimensional fermionic systems, close to band edges, the zero temperature conductance scales as $1/N^2$, where $N$ is the system length. This universal subdiffusive scaling of conductance at band edges has been tied to an exceptional point (EP) of the transfer matrix of the system that occur at every band edge. Further, in presence of bulk dephasing probes, this EP has been shown to lead to a counterintuitive superballistic scaling of conductance, where the conductance increases with $N$ over a finite but large regime of system lengths. In this work, we explore how these behaviors are affected by the order of the transfer matrix EP at the band edge. We consider a one-dimensional fermionic lattice chain with a finite range of hopping. Depending on the range of hopping and the hopping parameters, this system can feature band edges which correspond to arbitrarily higher order EPs of the associated transfer matrix. Using this system we establish in generality that, in absence of bulk dephasing, surprisingly, the universal $1/N^2$ scaling of conductance is completely unaffected by the order of the EP. This is despite the fact that existence of transfer matrix EP is crucial for such behavior. In presence of bulk dephasing, however, the phase coherence length, the extent of the superballisitic scaling regime and the exponent of superballistic scaling, all encode the order of the transfer matrix EP.

cond-mat.mes-hall↗
arXiv2024

Anomalous transport in long-ranged open quantum systems

We consider a one-dimensional fermionic lattice system with long-ranged power-law decaying hopping with exponent $α$. The system is further subjected to dephasing noise in the bulk. We investigate two variants of the problem: (i) an open quantum system where the setup is further subjected to boundary reservoirs enabling the scenario of a non-equilibrium steady state charge transport, and (ii) time dynamics of an initially localized single particle excitation in the absence of boundary reservoirs. In both variants, anomalous super-diffusive behavior is observed for $1< α< 1.5$, and for $α> 1.5$ the setup is effectively short-ranged and exhibits conventional diffusive transport. Our findings are supported by analytical calculations based on the multiple-scale analysis technique that leads to the emergence of a fractional diffusion equation for the density profile. Our study unravels an interesting interplay between long-range interaction and dephasing mechanism that could result in the emergence of unconventional behaviour in open quantum systems.

cond-mat.stat-mech↗
arXiv2023

Quantum coherent control of nonlinear thermoelectric transport in a triple-dot Aharonov-Bohm heat engine

We investigate the role of quantum coherence and higher harmonics resulting from multiple-path interference in nonlinear thermoelectricity in a two-terminal triangular triple-dot Aharonov-Bohm (AB) interferometer. We quantify the trade-off between efficiency and power in the nonlinear regime of our simple setup comprising three non-interacting quantum dots (two connected to two biased metallic reservoirs) placed at the vertex of an equilateral triangle, and a magnetic flux $Φ$ pierces it perpendicularly. For a spatially symmetric setup, we achieve optimal efficiency and power output when the inter-dot tunneling strength is comparable to the dot-lead coupling, AB phase $ϕ=π/2$. Our analysis reveals that the presence of higher harmonics is necessary but not sufficient to achieve optimal power output. The maximal constructive interference represented by three close-packed resonance peaks of the unit transmission can enhance the power output ($P_{max}\sim 2.35\,\mathrm{fW}$) almost 3.5 times as compared to the case where only a single channel participates in the transport, and the corresponding efficiency is about $0.80η_{c}$ where $η_{c}$ is the Carnot efficiency. Geometric asymmetries and their effects on efficiency and power output are also investigated. An asymmetric setup characterized by the ratio of the coupling to the source and the drain terminals ($x$) can further enhance the maximum power output $P_{max}\sim 3.85\,\mathrm{fW}$ for $x=1.5$ with the same efficiency as that of the symmetric case. Our investigation reveals that the output power and efficiency are optimal in the wide-band limit. The power output is significantly reduced for the narrow-band case. On the other hand, disorder effects radically reduce the performance of the heat engine.

cond-mat.mes-hall↗
arXiv2023

Environment assisted superballistic scaling of conductance

We find that, in the presence of weak incoherent effects from surrounding environments, the zero temperature conductance of nearest neighbour tight-binding chains exhibits a counter-intuitive power-law growth with system length at band-edges, indicating superballistic scaling. This fascinating environment assisted superballistic scaling of conductance occurs over a finite but extended regime of system lengths. This scaling regime can be systematically expanded by decreasing the coupling to the surrounding environments. There is no corresponding analog of this behavior for isolated systems. This superballistic scaling stems from an intricate interplay of incoherent effects from surrounding environments and exceptional points of the system's transfer matrix that occur at every band-edge.

cond-mat.mes-hall↗
arXiv2023

Exceptional hypersurfaces of transfer matrices of finite-range lattice models and their consequences on quantum transport properties

We investigate the emergence and corresponding nature of exceptional points located on exceptional hyper-surfaces of non-hermitian transfer matrices for finite-range one-dimensional lattice models. We unravel the non-trivial role of these exceptional points in determining the system size scaling of electrical conductance in non-equilibrium steady state. We observe that the band edges of the system always correspond to the transfer matrix exceptional points. Interestingly, albeit the lower band edge always occurs at wave-vector $k=0$, the upper band edge may or may not correspond to $k=π$. Nonetheless, in all the cases, the system exhibits universal subdiffusive transport for conductance at every band edge with scaling $N^{-b}$ with scaling exponent $b= 2$. However, for cases when the upper band edge is not located at $k=π$, the conductance features interesting oscillations with overall $N^{-2}$ scaling. Our work further reveals that this setup is uniquely suited to systematically generate higher order transfer matrix exceptional points at upper band edge when one considers finite range hoppings beyond nearest neighbour. Additional exceptional points other than those at band edges are shown to occur, although interestingly, these do not give rise to anomalous transport.

cond-mat.mes-hall↗
arXiv2023

Impact of dephasing on non-equilibrium steady-state transport in fermionic chains with long-range hopping

Quantum transport in a non-equilibrium setting plays a fundamental role in understanding the properties of systems ranging from quantum devices to biological systems. Dephasing -- a key aspect of out-of-equilibrium systems -- arises from the interactions with the noisy environment and can profoundly modify transport features. Here, we investigate the impact of dephasing on the non-equilibrium steady-state transport properties of non-interacting fermions on a one-dimensional lattice with long-range hopping ($\sim \frac{1}{r^α}$). We show the emergence of distinct transport regimes as the long-range hopping parameter $α$ is tuned. In the short-range limit ($α\gg 1$), transport is diffusive, while for the long-range limit ($α\sim \mathcal{O}(1)$), we observe a super-diffusive transport regime. Using the numerical simulation of the Lindblad master equation, and corroborated with the analysis of the current operator norm, we identify a critical long-range hopping parameter, $α_c \approx 1.5$, below which super-diffusive transport becomes evident that quickly becomes independent of the dephasing strength. Interstingly, within the super-diffusive regime, we find a crossover from logarithmic to power-law system-size dependence in the non-equilibrium steady-state resistance when $α$ varies from $α\leq 1$ to $α\lesssim 1.5$. Our results, thus, elucidate the intricate balance between dephasing and unitary dynamics, revealing novel steady-state transport features.

quant-ph↗
arXiv2023

Impact of dephasing probes on incommensurate lattices

We investigate open quantum dynamics for a one-dimensional incommensurate Aubry-André-Harper lattice chain, a part of which is initially filled with electrons and is further connected to dephasing probes at the filled lattice sites. This setup is akin to a step-initial configuration where the non-zero part of the step is subjected to dephasing. We investigate the quantum dynamics of local electron density, the scaling of the density front as a function of time both inside and outside of the initial step, and the growth of the total number of electrons outside the step. We analyze these quantities in all three regimes, namely, the de-localized, critical, and localized phases of the underlying lattice. Outside the initial step, we observe that the density front spreads according to the underlying nature of single-particle states of the lattice, for both the de-localized and critical phases. For the localized phase, the spread of the density front hints at a logarithmic behaviour in time that has no parallel in the isolated case (\emph{i.e.}, in the absence of probes). Inside the initial step, due to the presence of the probes, the density front spreads in a diffusive manner for all the phases. This combination of rich and different dynamical behaviour, outside and inside the initial step, results in the emergence of mixed dynamical phases. While the total occupation of electrons remains conserved, the value outside or inside the initial step turns out to have a rich dynamical behaviour. Our work is widely adaptable and has interesting consequences when disordered/quasi-disordered systems are subjected to a thermodynamically large number of probes.

cond-mat.stat-mech↗
arXiv2023

Study of non-equilibrium Green's functions beyond Born approximation in open quantum systems

We provide a systematic approach to compute different kinds of non-equilibrium Green's functions for open quantum systems which are essentially two-point correlation functions in time. We reveal that the definition of Green's functions based on the Born approximation does not provide the correct results in the leading order of the system-bath coupling. We next provide a systematic correction term in Green's functions by going beyond the Born approximation and incorporating a finite correlation between the system and the bath. We primarily focus on two paradigmatic models of open quantum systems, namely, the dissipative Caldeira-Leggett model and the dissipative spin-boson model. We show that the inclusion of such a correction correctly reproduces the Kadanoff-Baym type equation for the so-called lesser or greater components of the Green's functions and provides the correct long-time result up to the first non-zero order of the system-bath coupling, satisfying the detailed balance condition in thermal equilibrium. We further extend our study to a system coupled to multiple reservoirs simultaneously that are maintained at different temperatures and obtain expressions for non-equilibrium steady-state energy current, once again correct up to the first non-zero order of the system-bath coupling.

cond-mat.stat-mech↗
arXiv2023

Precision bound and optimal control in periodically modulated continuous quantum thermal machines

We use Floquet formalism to study fluctuations in periodically modulated continuous quantum thermal machines. We present a generic theory for such machines, followed by specific examples of sinusoidal, optimal, and circular modulations respectively. The thermodynamic uncertainty relations (TUR) hold for all modulations considered. Interestingly, in the case of sinusoidal modulation, the TUR ratio assumes a minimum at the heat engine to refrigerator transition point, while the Chopped Random Basis (CRAB) optimization protocol allows us to keep the ratio small for a wide range of modulation frequencies. Furthermore, our numerical analysis suggests that TUR can show signatures of heat engine to refrigerator transition, for more generic modulation schemes. We also study bounds in fluctuations in the efficiencies of such machines; our results indicate that fluctuations in efficiencies are bounded from above for a refrigerator, and from below for an engine. Overall, this study emphasizes the crucial role played by different modulation schemes in designing practical quantum thermal machines.

quant-ph↗
arXiv2023

Full statistics of non-equilibrium heat and work for many-body quantum Otto engines and universal bounds: A non-equilibrium Green's function approach

We consider a generic four-stroke quantum Otto engine consisting of two unitary and two thermalization strokes with an arbitrary many-body working medium. Using the Schwinger-Keldysh non-equilibrium Green's function formalism, we provide an analytical expression for the cumulant generating function corresponding to the joint probability distribution of non-equilibrium work and heat. The obtained result is valid up to the second order of the external driving amplitude. We then focus on the linear response limit and obtain Onsager's transport coefficients for the generic Otto cycle and showed that the traditional fluctuation-dissipation relation for the total work is violated in the quantum domain, whereas for heat it is preserved. This leads to remarkable consequences in obtaining universal constraints on heat and work fluctuations for engine and refrigerator regimes of the Otto cycle and further allows us to make connections to the thermodynamic uncertainty relations. These findings are illustrated using a paradigmatic model that can be feasibly implemented in experiments.

cond-mat.stat-mech↗
arXiv2023

Study of bounds on non-equilibrium fluctuations for asymmetrically driven quantum Otto engine

For a four-stroke asymmetrically driven quantum Otto engine with working medium modeled by a single qubit, we study the bounds on non-equilibrium fluctuations of work and heat. We find strict relations between the fluctuations of work and individual heat for hot and cold reservoirs in arbitrary operational regimes. Focusing on the engine regime, we show that the ratio of non-equilibrium fluctuations of output work to input heat from the hot reservoir is both upper and lower bounded. As a consequence, we establish hierarchical relation between the relative fluctuations of work and heat for both cold and hot reservoirs and further make a connection with the thermodynamic uncertainty relations. We discuss the fate of these bounds also in the refrigerator regime. The reported bounds, for such asymmetrically driven engines, emerge once both the time-forward and the corresponding reversed cycles of the engine are considered on an equal footing. We also extend our study and report bounds for a parametrically driven harmonic oscillator Otto engine.

cond-mat.stat-mech↗
arXiv2023

Modified quantum regression theorem and consistency with Kubo-Martin-Schwinger condition

We show that the long-time limit of the two-point correlation function obtained via the standard quantum regression theorem, a standard tool to compute correlation functions in open quantum systems, does not respect the Kubo-Martin-Schwinger equilibrium condition to the non-zero order of the system-bath coupling. We then follow the recently developed Heisenberg operator method for open quantum systems and by applying a ``{\it weak}" Markov approximation, derive a new modified version of the quantum regression theorem that not only respects the KMS condition but further predicts exact answers for certain paradigmatic models in specific limits. We also show that in cases where the modified quantum regression theorem does not match with exact answers, it always performs better than the standard quantum regression theorem.

quant-ph↗
arXiv2023

Universal subdiffusive behavior at band edges from transfer matrix exceptional points

We discover a deep connection between parity-time (PT) symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of $2 \times 2$ transfer matrices. We find that these non-Hermitian matrices have a symmetry exactly analogous to the PT-symmetry of balanced-gain-loss optical systems, and hence show analogous transitions across exceptional points. We show that the exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum. When connected to two zero temperature baths at two ends, this consequently leads to subdiffusive scaling of conductance with system size, with an exponent $2$, if the chemical potential of the baths are equal to the band edges. We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge. Remarkably, this feature is analogous to transition across a mobility edge in quasiperiodic systems. This behavior is universal, irrespective of the details of the periodic potential and the number of bands of the underlying lattice. It, however, has no analog in absence of the baths.

quant-ph↗