arXiv subjects

Colin Benjamin

Publications and source records attributed to Colin Benjamin.

At least 37 records · Page 2Linked to original sources

arXiv2024

Game susceptibility, Correlation and Payoff capacity as a measure of Cooperative behavior in the thermodynamic limit of some Social dilemmas

Analytically, finding the origins of cooperative behavior in infinite-player games is an exciting topic of current interest. In this paper, we compare three analytical methods, i.e., Nash equilibrium mapping (NEM), Darwinian selection (DS) and Aggregate selection (AS), with a numerical Agent based method (ABM) via the game susceptibility, correlation, and payoff capacity as indicators of cooperative behaviour. While the analytical NEM model shows excellent agreement with the numerical ABM, the other analytical models, like AS and DS, show notable divergence with ABM in the thermodynamic limit for the indicators in question. Previously, cooperative behavior was studied by considering game magnetization and individual players' average payoff as indicators. This paper shows that game susceptibility, correlation, and payoff capacity can aid in understanding cooperative behavior in social dilemmas in the thermodynamic limit. The results obtained via NEM and ABM are in good agreement for all three indicators in question, for both Hawk-Dove and the Public goods games. After comparing the results obtained for all five indicators, we see that individual players' average payoff and payoff capacity serve as the best indicators to study cooperative behavior among players in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2024

Reaching Van den Broeck limit in linear response and Whitney limit in nonlinear response in edge mode quantum thermoelectrics and refrigeration

Quantum heat engines and quantum refrigerators are proposed in three-terminal quantum Hall (QH) and quantum spin Hall (QSH) setups with a voltage-temperature probe in both the linear and nonlinear transport regimes. In the linear response regime, we find that efficiency at maximum power approaches the Van den Broeck limit in both QH and QSH setups. Similarly, in nonlinear response, we find that efficiency at maximum power reaches the Whitney bounds. This is for the first time, we see that in the same setup and using quantum point contacts, the thermoelectric efficiency limits in linear and nonlinear response being achieved.

cond-mat.mes-hall↗

arXiv2024

Majorana Thermoelectrics and Refrigeration

A two-terminal quantum spin-Hall heat engine and refrigerator with embedded Majorana bound states (MBS) is analyzed for optimality in thermoelectric performance using the Landaeur-Buttiker approach. This investigation can be an effective tool to detect MBS. Furthermore, the occurrence of MBS can enhance the performance to rival, as well as outperform, some modern nanoscale quantum heat engines and quantum refrigerators. The optimal performance of this MBS quantum heat engine and quantum refrigerator can be further enhanced by an Aharonov-Bohm flux.

cond-mat.mes-hall↗

arXiv2024

Majorana fermion induced power-law scaling in the violations of the Wiedemann-Franz law

Violation of the Wiedemann-Franz law in a 2D topological insulator due to Majorana bound states is studied via the Lorenz ratio in the single-particle picture. We study the scaling of the Lorenz ratio in the presence and absence of Majorana bound states with inelastic scattering modeled using a Buttiker voltage-temperature probe. We compare our results with that seen in a quantum dot junction in the Luttinger liquid picture operating in the topological Kondo regime. We explore the scaling of the Lorentz ratio in our setup when either phase and momentum relaxation or phase relaxation is present. This scaling differs from that predicted by the Luttinger liquid picture for both uncoupled and coupled Majorana cases.

cond-mat.mes-hall↗

arXiv2024

Quantum cryptographic protocols with dual messaging system via 2D alternate quantum walk of a genuine single-photon entangled state

A single-photon entangled state (or single-particle entangled state (SPES) in general) can offer a more secure way of encoding and processing quantum information than their multi-photon (or multi-particle) counterparts. The SPES generated via a 2D alternate quantum-walk setup from initially separable states can be either 3-way or 2-way entangled. This letter shows that the generated genuine three-way and nonlocal two-way SPES can be used as cryptographic keys to securely encode two distinct messages simultaneously. We detail the message encryption-decryption steps and show the resilience of the 3-way and 2-way SPES-based cryptographic protocols against eavesdropper attacks like intercept-and-resend and man-in-the-middle. We also detail the experimental realization of these protocols using a single photon, with the three degrees of freedom being OAM, path, and polarization. We have proved that the protocols have unconditional security for quantum communication tasks. The ability to simultaneously encode two distinct messages using the generated SPES showcases the versatility and efficiency of the proposed cryptographic protocol. This capability could significantly improve the throughput of quantum communication systems.

quant-ph↗

arXiv2024

Yu-Shiba-Rusinov bound states boost odd-frequency superconductivity

We predict that the occurence of zero energy Yu-Shiba-Rusinov(YSR) bound states in two different setups, metal-spin flipper-metal-s-wave superconductor ($N_{1}-sf-N_{2}-S$) and superconductor-metal-spin flipper-metal-superconductor ($S-N_{1}-sf-N_{2}-S$) junctions, can generate multi-fold enhancement of surface-induced odd-frequency superconductivity. On the other hand, in the absence of these bound states, even-frequency superconductivity dominates. Specifically, in a $S-N_{1}-sf-N_{2}-S$ Josephson junction, the emergence of zero energy YSR bound states leads to a $0-π$ junction transition and surface odd-frequency superconductivity dominance. Notably, odd-frequency superconductivity vanishes in the absence of YSR-bound states. Interestingly, the equal spin-triplet pairing is the dominant component in the surface induced odd-frequency superconductivity in both setups, which could have important implications for superconducting spintronics. Overall, our findings may help to detect the presence of YSR-bound states through the observation of surface induced odd-frequency superconductivity and contribute to a better understanding of their relationship.

cond-mat.supr-con↗

arXiv2024

Selection pressure/Noise driven cooperative behaviour in the thermodynamic limit of repeated games

Consider the scenario where an infinite number of players (i.e., the \textit{thermodynamic} limit) find themselves in a Prisoner's dilemma type situation, in a \textit{repeated} setting. Is it reasonable to anticipate that, in these circumstances, cooperation will emerge? This paper addresses this question by examining the emergence of cooperative behaviour, in the presence of \textit{noise} (or, under \textit{selection pressure}), in repeated Prisoner's Dilemma games, involving strategies such as \textit{Tit-for-Tat}, \textit{Always Defect}, \textit{GRIM}, \textit{Win-Stay, Lose-Shift}, and others. To analyze these games, we employ a numerical Agent-Based Model (ABM) and compare it with the analytical Nash Equilibrium Mapping (NEM) technique, both based on the \textit{1D}-Ising chain. We use \textit{game magnetization} as an indicator of cooperative behaviour. A significant finding is that for some repeated games, a discontinuity in the game magnetization indicates a \textit{first}-order \textit{selection pressure/noise}-driven phase transition. The phase transition is particular to strategies where players do not severely punish a single defection. We also observe that in these particular cases, the phase transition critically depends on the number of \textit{rounds} the game is played in the thermodynamic limit. For all five games, we find that both ABM and NEM, in conjunction with game magnetization, provide crucial inputs on how cooperative behaviour can emerge in an infinite-player repeated Prisoner's dilemma game.

cond-mat.stat-mech↗

arXiv2024

Surface induced odd-frequency spin-triplet superconductivity as a veritable signature of Majorana bound states

We predict surface-induced odd-frequency (odd-$ν$) spin-triplet superconducting pairing can be a veritable signature of Majorana bound states (MBS) in a Josephson nodal $p$-wave superconductor ($p_{x}$)-spin flipper (SF)-nodal $p$-wave superconductor ($p_{x}$) junction. Remarkably, in a $p_{x}$-SF-$p_{x}$ Josephson junction three distinct phases emerge: the topological phase featuring MBS, the topological phase without MBS, and the trivial phase devoid of MBS. Surface odd-$ν$ spin-triplet pairing is induced only in the topological regime when MBS appears. In contrast, surface-induced even-frequency (even-$ν$) spin-triplet pairing is finite regardless of the existence of MBS. Importantly, we find the surface induced odd-$ν$ spin-triplet pairing is immune to disorder in the topological phase featuring MBS, while in the trivial phase the surface induced even-$ν$ spin-triplet pairing is affected by disorder. Our study offers a potential means for distinguishing the topological phase featuring MBS from both the trivial phase as well as the topological phase devoid of MBS, primarily through the observation of induced surface odd-$ν$ spin-triplet superconductivity.

cond-mat.mes-hall↗

arXiv2024

Probing Majorana Bound States via Thermoelectric Transport

We propose a set of thermoelectric experiments based on Aharonov-Bohm interferometry to probe Majorana bound states (MBS), which are generated in 2D topological insulators (TI) in the presence of superconducting and ferromagnetic correlations via the proximity effect. The existence and nature (coupled or uncoupled) of these MBS can be determined by studying the charge and heat transport, specifically, the behavior of various thermoelectric coefficients like the Seebeck coefficient, Peltier coefficient, thermal conductance, and violations of Wiedemann-Franz law as a function of the Fermi energy and Aharonov-Bohm flux piercing the TI ring with the embedded MBS.

cond-mat.mes-hall↗

arXiv2024

Resolving degeneracies in Google search via quantum stochastic walks

The Internet is one of the most valuable technologies invented to date. Among them, Google is the most widely used search engine. The PageRank algorithm is the backbone of Google search, ranking web pages according to relevance and recency. We employ quantum stochastic walks (QSWs) to improve the classical PageRank (CPR) algorithm based on classical continuous time random walks. We implement QSW via two schemes: only incoherence and dephasing with incoherence. PageRank using QSW with only incoherence or QSW with dephasing and incoherence best resolves degeneracies that are unresolvable via CPR and with a convergence time comparable to that for CPR, which is generally the minimum. For some networks, the two QSW schemes obtain a convergence time lower than CPR and an almost degeneracy-free ranking compared to CPR.

quant-ph↗

arXiv2023

Honing in on a topological zero-bias conductance peak

A popular signature of Majorana bound states in topological superconductors is the zero-energy conductance peak with a height of $2e^2/h$. However, a similar zero energy conductance peak with almost the same height can also arise due to non-topological reasons. Here we show that these trivial and topological zero energy conductance peaks can be distinguished via the zero energy local density of states and local magnetization density of states. We find that the zero-energy local density of states exhibits oscillations with a finite period for a trivial zero-bias conductance peak. In contrast, these oscillations disappear for the topological zero-bias conductance peak. On the other hand, zero energy local magnetization density of states shows a periodic oscillation for trivial zero-bias conductance peak, while for topological ZBCP, they vanish. Our results suggest that zero-energy local density of states and local magnetization density of states can be used as an experimental probe to distinguish trivial zero energy conductance peak from topological zero energy conductance peak.

cond-mat.mes-hall↗

arXiv2023

Switching global correlations on and off in a many-body quantum state by tuning local entanglement

A quantum many-body state built on a classical 1D Ising model with locally entangled qubits is considered. This setup can model an infinite-player quantum Prisoner's dilemma game with each site representing two entangled players (or qubits). The local entanglement $γ$ between two qubits placed on a site in the 1D Ising model and classical coupling between adjacent sites of the Ising model has an apposite influence on qubits. It points to a counter-intuitive situation wherein local entanglement at a site can exactly cancel global correlations, signaling an artificial quantum many-body state wherein, by locally tuning the entanglement at a particular site, one can transition from a strongly correlated quantum state to an uncorrelated quantum state and then to a correlated classical state. In other words, we can simulate a state similar to a Type II superconducting state via local tuning of entanglement in a 1D Ising chain with entangled qubits.

quant-ph↗

arXiv2023

Recurrent generation of maximally entangled single particle states via quantum walks on cyclic graphs

Maximally entangled single-particle states (MESPS) are opening new possibilities in quantum technology as they have the potential to encode more information and are robust to decoherence compared to their nonlocal two-particle counterparts. We find that a single coin can generate MESPS at recurrent time steps (periodically) via discrete-time quantum walks on both $4$ and $8$ site cyclic graphs. This scheme is resource-saving with possibly the most straightforward experimental realization since the same coin is applied at each time step. We also show that recurrent MESPS can be generated on any arbitrary $k$ site cyclic graph, $k\in\{3,4,5,8\}$ via effective-single (Identity and arbitrary coin) or two coin evolution sequences. Beyond their use in fundamental research, we propose an application of the generated MESPS in quantum cryptography protocols. MESPS as cryptographic keys can strengthen quantum-secure communication.

quant-ph↗

arXiv2023

Finite temperature quantum noise correlations as a probe for topological helical edge modes

The distinction between chiral, trivial helical, and topological helical edge modes can be effectively made using quantum noise measurements at finite temperatures. Quantum noise measurements consist of mainly two components. The first is thermal noise, whose provenance is thermal fluctuations, and the second is shot noise, whose origin is the quantum nature of charge particles. Studying these edge modes at finite temperatures is important as it more accurately reflects the conditions in real-world experiments. Additionally, we have verified that our results for finite temperature quantum noise correlations are valid at finite frequencies too.

cond-mat.mes-hall↗

arXiv2023

Nash equilibrium mapping vs Hamiltonian dynamics vs Darwinian evolution for some social dilemma games in the thermodynamic limit

How cooperation evolves and manifests itself in the thermodynamic or infinite player limit of social dilemma games is a matter of intense speculation. Various analytical methods have been proposed to analyze the thermodynamic limit of social dilemmas. In this work, we compare two analytical methods, i.e., Darwinian evolution and Nash equilibrium mapping, with a numerical agent-based approach. For completeness, we also give results for another analytical method, Hamiltonian dynamics. In contrast to Hamiltonian dynamics, which involves the maximization of payoffs of all individuals, in Darwinian evolution, the payoff of a single player is maximized with respect to its interaction with the nearest neighbor. While the Hamiltonian dynamics method utterly fails as compared to Nash equilibrium mapping, the Darwinian evolution method gives a false positive for game magnetization -- the net difference between the fraction of cooperators and defectors -- when payoffs obey the condition a + d = b + c, wherein a,d represents the diagonal elements and b,c the off-diagonal elements in a symmetric social dilemma game payoff matrix. When either a + d =/= b + c or when one looks at the average payoff per player, the Darwinian evolution method fails, much like the Hamiltonian dynamics approach. On the other hand, the Nash equilibrium mapping and numerical agent-based method agree well for both game magnetization and average payoff per player for the social dilemmas in question, i.e., the Hawk-Dove game and the Public goods game. This paper thus brings to light the inconsistency of the Darwinian evolution method vis-a-vis both Nash equilibrium mapping and a numerical agent-based approach.

cond-mat.stat-mech↗

arXiv2023

Vaccination Dilemma in the thermodynamic limit

The vaccination game is a social dilemma that refers to the conundrum individuals face (to get immunized or not) when the population is exposed to an infectious disease. The model has recently gained much traction due to the COVID-19 pandemic since the public perception of vaccines plays a significant role in disease dynamics. This paper studies the vaccination game in the thermodynamic limit with an analytical method derived from the 1D Ising model called Nash equilibrium mapping. The individual dilemma regarding Vaccination comes from an internal conflict wherein one tries to balance the perceived advantages of immunizing with the apparent risks associated with Vaccination which they hear through different news media. We compare the results of Nash equilibrium(NE) mapping to other 1D Ising-based models, namely Darwinian evolution and agent-based simulation. This study aims to analyze the behaviour of an infinite population regarding what fraction of people choose to vaccinate or not vaccinate. While Nash equilibrium mapping and agent-based simulation agree mostly, Darwinian evolution strays far from the two models. It fails to predict the equilibrium behaviour of players in the population reasonably. We apply the results of our study to analyze the Astra-Zeneca(AZ) COVID-19 vaccine risk versus disease deaths debate, both via NE mapping and agent-based method. Both predict near 100% AZ vaccine coverage for people above 40, notwithstanding the risk. At the same time, younger people show a slight reluctance. We predict that while government intervention via vaccination mandates and advertisement campaigns is unnecessary for the older population, for the younger population (ages: 20-39), some encouragement from the government via media campaigns and vaccine mandates may be necessary.

physics.soc-ph↗

arXiv2022

Generating highly entangled states via discrete-time quantum walks with Parrondo sequences

Quantum entanglement has multiple applications in quantum information processing. Developing methods to generate highly entangled states independent of initial conditions is an essential task. Herein we aim to generate highly entangled states via discrete-time quantum walks. We propose deterministic Parrondo sequences that generate states that are generally much more entangled than states produced by sequences using only one of the two coins. We show that some Parrondo sequences generate highly entangled states, which are independent of the phase of the initial state used and further lead to maximally entangled states in some cases. We study Parrondo sequences for a small number of time steps and the asymptotic limit of a large number of time steps.

quant-ph↗

arXiv2022

Impurity reveals distinct operational phases in quantum thermodynamic cycles

We analyze the effect of impurity on the work output and efficiency of quantum Otto and quantum Carnot heat cycles, modeled as a single quantum particle in an infinite square well (ISW) potential, which is the working substance. We solve this quantum mechanical system perturbatively up to first and second order in strength of the impurity for strong and weak coupling regimes, respectively. We derive the analytical expressions of work and efficiency for the strong coupling regime to the first order in the strength parameter. The threshold value of the strength parameter in weak coupling is obtained up to which the numerical result agrees with the perturbative result for a repulsive and attractive impurity. To our surprise, an embedded impurity unlocks new operational phases in the system, such as a quantum heat engine, quantum refrigerator, and quantum cold pump. In addition, the efficiency of the quantum Otto heat engine is seen to reach Carnot efficiency for some parameter regimes. The cooling power and coefficient of performance of the quantum refrigerator and quantum cold pump are non-trivially affected by the impurity.

quant-ph↗