Pub Date : 2024-08-12DOI: 10.1103/physrevresearch.6.033159
Marco Mancastroppa, Alessandro Vezzani, Vittoria Colizza, Raffaella Burioni
Human behavior strongly influences the spread of infectious diseases: understanding the interplay between epidemic dynamics and adaptive behaviors is essential to improve response strategies to epidemics, with the goal of containing the epidemic while preserving a sufficient level of operativeness in the population. Through activity-driven temporal networks, we formulate a general framework which models a wide range of adaptive behaviors and mitigation strategies, observed in real populations. We analytically derive the conditions for a widespread diffusion of epidemics in the presence of arbitrary adaptive behaviors, highlighting the crucial role of correlations between agents behavior in the infected and in the susceptible state. We focus on the effects of sick leave, comparing the effectiveness of different strategies in reducing the impact of the epidemic and preserving the system operativeness. We show the critical relevance of heterogeneity in individual behavior: in homogeneous networks, all sick-leave strategies are equivalent and poorly effective, while in heterogeneous networks, strategies targeting the most vulnerable nodes are able to effectively mitigate the epidemic, also avoiding a deterioration in system activity and maintaining a low level of absenteeism. Interestingly, with targeted strategies both the minimum of population activity and the maximum of absenteeism anticipate the infection peak, which is effectively flattened and delayed, so that full operativeness is almost restored when the infection peak arrives. We also provide realistic estimates of the model parameters for influenza-like illness, thereby suggesting strategies for managing epidemics and absenteeism in realistic populations.
{"title":"Preserving system activity while controlling epidemic spreading in adaptive temporal networks","authors":"Marco Mancastroppa, Alessandro Vezzani, Vittoria Colizza, Raffaella Burioni","doi":"10.1103/physrevresearch.6.033159","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033159","url":null,"abstract":"Human behavior strongly influences the spread of infectious diseases: understanding the interplay between epidemic dynamics and adaptive behaviors is essential to improve response strategies to epidemics, with the goal of containing the epidemic while preserving a sufficient level of operativeness in the population. Through activity-driven temporal networks, we formulate a general framework which models a wide range of adaptive behaviors and mitigation strategies, observed in real populations. We analytically derive the conditions for a widespread diffusion of epidemics in the presence of arbitrary adaptive behaviors, highlighting the crucial role of correlations between agents behavior in the infected and in the susceptible state. We focus on the effects of sick leave, comparing the effectiveness of different strategies in reducing the impact of the epidemic and preserving the system operativeness. We show the critical relevance of heterogeneity in individual behavior: in homogeneous networks, all sick-leave strategies are equivalent and poorly effective, while in heterogeneous networks, strategies targeting the most vulnerable nodes are able to effectively mitigate the epidemic, also avoiding a deterioration in system activity and maintaining a low level of absenteeism. Interestingly, with targeted strategies both the minimum of population activity and the maximum of absenteeism anticipate the infection peak, which is effectively flattened and delayed, so that full operativeness is almost restored when the infection peak arrives. We also provide realistic estimates of the model parameters for influenza-like illness, thereby suggesting strategies for managing epidemics and absenteeism in realistic populations.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141946067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-12DOI: 10.1103/physrevresearch.6.033161
Yohei Onuki, Antoine Venaille, Pierre Delplace
Bulk-edge correspondence is a cornerstone in topological physics, establishing a connection between the number of unidirectional edge modes in physical space and a Chern number, an integer that counts phase singularities of the eigenmodes in parameter space. In continuous media, violation of this correspondence has been reported when some of the frequency wave bands are unbounded, resulting in weak topological protection of chiral edge states. Here, we propose a strategy to reestablish strong bulk-edge correspondence in incompressible rotating stratified flows, taking advantage of a natural cutoff frequency provided by density stratification. The key idea involves the introduction of an auxiliary field to handle the divergence-free constraint. This approach highlights the resilience of internal coastal Kelvin waves near vertical walls under varying boundary conditions.
{"title":"Bulk-edge correspondence recovered in incompressible geophysical flows","authors":"Yohei Onuki, Antoine Venaille, Pierre Delplace","doi":"10.1103/physrevresearch.6.033161","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033161","url":null,"abstract":"Bulk-edge correspondence is a cornerstone in topological physics, establishing a connection between the number of unidirectional edge modes in physical space and a Chern number, an integer that counts phase singularities of the eigenmodes in parameter space. In continuous media, violation of this correspondence has been reported when some of the frequency wave bands are unbounded, resulting in weak topological protection of chiral edge states. Here, we propose a strategy to reestablish strong bulk-edge correspondence in incompressible rotating stratified flows, taking advantage of a natural cutoff frequency provided by density stratification. The key idea involves the introduction of an auxiliary field to handle the divergence-free constraint. This approach highlights the resilience of internal coastal Kelvin waves near vertical walls under varying boundary conditions.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":"86 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141946069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Loop extrusion is one of the main processes shaping chromosome organization across the cell cycle, yet its role in regulating deoxyribonucleic acid (DNA) entanglement and nucleoplasm viscoelasticity remains overlooked. We simulate entangled solutions of linear polymers under the action of generic loop extruding factors (LEFs) with a model that fully accounts for topological constraints and LEF-DNA uncrossability. We discover that extrusion drives the formation of bottlebrushlike structures which significantly lower the entanglement and effective viscosity of the system through an active fluidification mechanism. Interestingly, this fluidification displays an optimum at one LEF every 300–3000 base pairs. In marked contrast with entangled linear chains, the viscosity of extruded chains scales linearly with polymer length, yielding up to 1000-fold fluidification in our system. Our results illuminate how intrachain loop extrusion contributes to actively modulate genome entanglement and viscoelasticity in vivo.
{"title":"Fluidification of entangled polymers by loop extrusion","authors":"Filippo Conforto, Yair Gutierrez Fosado, Davide Michieletto","doi":"10.1103/physrevresearch.6.033160","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033160","url":null,"abstract":"Loop extrusion is one of the main processes shaping chromosome organization across the cell cycle, yet its role in regulating deoxyribonucleic acid (DNA) entanglement and nucleoplasm viscoelasticity remains overlooked. We simulate entangled solutions of linear polymers under the action of generic loop extruding factors (LEFs) with a model that fully accounts for topological constraints and LEF-DNA uncrossability. We discover that extrusion drives the formation of bottlebrushlike structures which significantly lower the entanglement and effective viscosity of the system through an active fluidification mechanism. Interestingly, this fluidification displays an optimum at one LEF every 300–3000 base pairs. In marked contrast with entangled linear chains, the viscosity of extruded chains scales linearly with polymer length, yielding up to 1000-fold fluidification in our system. Our results illuminate how intrachain loop extrusion contributes to actively modulate genome entanglement and viscoelasticity <i>in vivo</i>.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":"94 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141946066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-12DOI: 10.1103/physrevresearch.6.l032035
Henning U. Voss, Douglas J. Ballon
It is shown on the examples of Moore and Gosper curves that two spatially shifted or twisted, preasymptotic space-filling curves can produce large-scale superstructures akin to moiré patterns. To study physical phenomena emerging from these patterns, a geometrical coupling coefficient based on the Neumann integral is introduced. It is found that moiré patterns appear most defined at the peaks of those coefficients. A physical interpretation of these coefficients as a measure for inductive coupling between radiofrequency resonators leads to a design principle for strongly overlapping resonators with vanishing mutual inductance, which might be interesting for applications in MRI. These findings are demonstrated in graphical, numerical, and physical experiments.
{"title":"Moiré patterns of space-filling curves","authors":"Henning U. Voss, Douglas J. Ballon","doi":"10.1103/physrevresearch.6.l032035","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.l032035","url":null,"abstract":"It is shown on the examples of Moore and Gosper curves that two spatially shifted or twisted, preasymptotic space-filling curves can produce large-scale superstructures akin to moiré patterns. To study physical phenomena emerging from these patterns, a geometrical coupling coefficient based on the Neumann integral is introduced. It is found that moiré patterns appear most defined at the peaks of those coefficients. A physical interpretation of these coefficients as a measure for inductive coupling between radiofrequency resonators leads to a design principle for strongly overlapping resonators with vanishing mutual inductance, which might be interesting for applications in MRI. These findings are demonstrated in graphical, numerical, and physical experiments.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141946045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-12DOI: 10.1103/physrevresearch.6.033162
Rémi Goerlich, Tommer D. Keidar, Yael Roichman
We present and characterize a method to accelerate the relaxation of a Brownian object between two distinct equilibrium states. Instead of relying on a deterministic time-dependent control parameter, we use stochastic resetting to guide and accelerate the transient evolution. The protocol is investigated theoretically, and its thermodynamic cost is evaluated with the tools of stochastic thermodynamics. Remarkably, we show that stochastic resetting significantly accelerates the relaxation to the final state. This stochastic protocol exhibits energetic and temporal characteristics that align with the scales observed in previously investigated deterministic protocols. Moreover, it expands the spectrum of stationary states that can be manipulated, incorporating new potential profiles achievable through experimentally viable protocols.
{"title":"Resetting as a swift equilibration protocol in an anharmonic potential","authors":"Rémi Goerlich, Tommer D. Keidar, Yael Roichman","doi":"10.1103/physrevresearch.6.033162","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033162","url":null,"abstract":"We present and characterize a method to accelerate the relaxation of a Brownian object between two distinct equilibrium states. Instead of relying on a deterministic time-dependent control parameter, we use stochastic resetting to guide and accelerate the transient evolution. The protocol is investigated theoretically, and its thermodynamic cost is evaluated with the tools of stochastic thermodynamics. Remarkably, we show that stochastic resetting significantly accelerates the relaxation to the final state. This stochastic protocol exhibits energetic and temporal characteristics that align with the scales observed in previously investigated deterministic protocols. Moreover, it expands the spectrum of stationary states that can be manipulated, incorporating new potential profiles achievable through experimentally viable protocols.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141946064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-12DOI: 10.1103/physrevresearch.6.033163
Austin Hoover, Jonathan C. Wong
Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the absence of direct measurements, the distribution must be tomographically reconstructed from its projections. In this paper, we highlight that such problems can be severely underdetermined and that entropy maximization is the most conservative solution strategy. We leverage normalizing flows—invertible generative models—to extend maximum-entropy tomography to six-dimensional phase space and perform numerical experiments to validate the model's performance. Our numerical experiments demonstrate consistency with exact two-dimensional maximum-entropy solutions and the ability to fit complicated six-dimensional distributions to large measurement sets in reasonable time.
{"title":"High-dimensional maximum-entropy phase space tomography using normalizing flows","authors":"Austin Hoover, Jonathan C. Wong","doi":"10.1103/physrevresearch.6.033163","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033163","url":null,"abstract":"Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the absence of direct measurements, the distribution must be tomographically reconstructed from its projections. In this paper, we highlight that such problems can be severely underdetermined and that entropy maximization is the most conservative solution strategy. We leverage <i>normalizing flows</i>—invertible generative models—to extend maximum-entropy tomography to six-dimensional phase space and perform numerical experiments to validate the model's performance. Our numerical experiments demonstrate consistency with exact two-dimensional maximum-entropy solutions and the ability to fit complicated six-dimensional distributions to large measurement sets in reasonable time.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141946063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-12DOI: 10.1103/physrevresearch.6.033157
Dijana Milosavljević, Helge Rosner, Annika Johansson
We present a detailed theoretical study of the electronic structure of hafnium tin HfSn crystallizing in a structure, renowned for the diversity of physical and peculiar topological properties. The chiral crystal structure of these materials protects multifold band crossings located at high-symmetry points. We employ density functional methods to reveal basic features of the band structure and Fermi surface topology of HfSn, on top of which a tight-binding model is built. The compound exhibits a fourfold band crossing pinned at the point. We investigate routes that can shift such crossings towards the Fermi level, offering a way to possibly tune the compound's properties. Specifically, we show that the energy position of the fourfold crossing can be easily manipulated via external perturbations such as strain and pressure. Considering that this point carries a topological charge larger than 1, such tuning is of great importance. We anticipate that the approach presented in the current study can be utilized to investigate symmetry-protected crossings in a wide class of materials.
{"title":"Electronic structure of noncentrosymmetric B20 compound HfSn and tuning of multifold band-crossing points","authors":"Dijana Milosavljević, Helge Rosner, Annika Johansson","doi":"10.1103/physrevresearch.6.033157","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033157","url":null,"abstract":"We present a detailed theoretical study of the electronic structure of hafnium tin HfSn crystallizing in a <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">B</mi><mn>20</mn></mrow></math> structure, renowned for the diversity of physical and peculiar topological properties. The chiral crystal structure of these materials protects multifold band crossings located at high-symmetry points. We employ density functional methods to reveal basic features of the band structure and Fermi surface topology of HfSn, on top of which a tight-binding model is built. The compound exhibits a fourfold band crossing pinned at the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"normal\">Γ</mi></math> point. We investigate routes that can shift such crossings towards the Fermi level, offering a way to possibly tune the compound's properties. Specifically, we show that the energy position of the fourfold crossing can be easily manipulated via external perturbations such as strain and pressure. Considering that this point carries a topological charge larger than 1, such tuning is of great importance. We anticipate that the approach presented in the current study can be utilized to investigate symmetry-protected crossings in a wide class of materials.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141946068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-12DOI: 10.1103/physrevresearch.6.033155
John F. Kam, Haiyue Kang, Charles D. Hill, Gary J. Mooney, Lloyd C. L. Hollenberg
As quantum technology advances and the size of quantum computers grow, it becomes increasingly important to understand the extent of quality in the devices. As large-scale entanglement is a quantum resource crucial for achieving quantum advantage, the challenge in its generation makes it a valuable benchmark for measuring the performance of universal quantum devices. In this paper, we study entanglement in Greenberger-Horne-Zeilinger (GHZ) and graph states prepared on the range of IBM Quantum devices. We generate GHZ states and investigate their coherence times with respect to state size and dynamical decoupling techniques. A GHZ fidelity of is measured on a 32-qubit GHZ state, certifying its genuine multipartite entanglement (GME). We show a substantial improvement in GHZ decoherence rates for a seven-qubit GHZ state after implementing dynamical decoupling, and observe a linear trend in the decoherence rate of for up to qubits, confirming the absence of superdecoherence. Additionally, we prepare and characterize fully bipartite entangled native-graph states on 22 superconducting quantum devices with qubit counts as high as 414 qubits, all active qubits of the 433-qubit IBM Osprey device. Analysis of the decay of two-qubit entanglement within the prepared states shows suppression of coherent noise signals with the implementation of dynamical decoupling techniques. Additionally, we observe that the entanglement in some qubit pairs oscillates over time, which is likely caused by residual ZZ-interactions. Characterizing entanglement in native-graph states, along with detecting entanglement oscillations, can be an effective approach to low-level device benchmarking that encapsulates two-qubit error rates along with additional sources of noise, with possible applications to quantum circuit compilation. We develop several tools to automate the preparation and entanglement characterization of GHZ and graph states. In particular, a method to characterize graph state bipartite entanglement using just 36 circuits, constant with respect to the number of qubits.
{"title":"Characterization of entanglement on superconducting quantum computers of up to 414 qubits","authors":"John F. Kam, Haiyue Kang, Charles D. Hill, Gary J. Mooney, Lloyd C. L. Hollenberg","doi":"10.1103/physrevresearch.6.033155","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033155","url":null,"abstract":"As quantum technology advances and the size of quantum computers grow, it becomes increasingly important to understand the extent of quality in the devices. As large-scale entanglement is a quantum resource crucial for achieving quantum advantage, the challenge in its generation makes it a valuable benchmark for measuring the performance of universal quantum devices. In this paper, we study entanglement in Greenberger-Horne-Zeilinger (GHZ) and graph states prepared on the range of IBM Quantum devices. We generate GHZ states and investigate their coherence times with respect to state size and dynamical decoupling techniques. A GHZ fidelity of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>0.519</mn><mo>±</mo><mn>0.014</mn></mrow></math> is measured on a 32-qubit GHZ state, certifying its genuine multipartite entanglement (GME). We show a substantial improvement in GHZ decoherence rates for a seven-qubit GHZ state after implementing dynamical decoupling, and observe a linear trend in the decoherence rate of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>α</mi><mo>=</mo><mrow><mo>(</mo><mn>7.13</mn><mi>N</mi><mo>+</mo><mn>5.54</mn><mo>)</mo></mrow><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mspace width=\"0.16em\"></mspace><mi>µ</mi><msup><mrow><mi mathvariant=\"normal\">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> for up to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>N</mi><mo>=</mo><mn>15</mn></mrow></math> qubits, confirming the absence of superdecoherence. Additionally, we prepare and characterize fully bipartite entangled native-graph states on 22 superconducting quantum devices with qubit counts as high as 414 qubits, all active qubits of the 433-qubit IBM Osprey device. Analysis of the decay of two-qubit entanglement within the prepared states shows suppression of coherent noise signals with the implementation of dynamical decoupling techniques. Additionally, we observe that the entanglement in some qubit pairs oscillates over time, which is likely caused by residual ZZ-interactions. Characterizing entanglement in native-graph states, along with detecting entanglement oscillations, can be an effective approach to low-level device benchmarking that encapsulates two-qubit error rates along with additional sources of noise, with possible applications to quantum circuit compilation. We develop several tools to automate the preparation and entanglement characterization of GHZ and graph states. In particular, a method to characterize graph state bipartite entanglement using just 36 circuits, constant with respect to the number of qubits.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141946071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-12DOI: 10.1103/physrevresearch.6.033156
Seyong Kim, Alexander Rothkopf
We construct a discrete non-Hermitian momentum operator, which implements faithfully the non-self-adjoint nature of momentum for a particle in a box. Its eigenfunctions are strictly limited to the interior of the box in the continuum limit, with the quarter wave as first nontrivial eigenstate. We show how to construct the corresponding Hermitian Hamiltonian for the infinite well as a concrete example to realize unitary dynamics. The resulting Hilbert space can be decomposed into a physical and unphysical subspace, which are mutually orthogonal. The physical subspace in the continuum limit reproduces that of the continuum theory and we give numerical evidence that the correct probability distributions for momentum and energy are recovered.
{"title":"Non-Hermitian momentum operator for the particle in a box","authors":"Seyong Kim, Alexander Rothkopf","doi":"10.1103/physrevresearch.6.033156","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033156","url":null,"abstract":"We construct a discrete non-Hermitian momentum operator, which implements faithfully the non-self-adjoint nature of momentum for a particle in a box. Its eigenfunctions are strictly limited to the interior of the box in the continuum limit, with the quarter wave as first nontrivial eigenstate. We show how to construct the corresponding Hermitian Hamiltonian for the infinite well as a concrete example to realize unitary dynamics. The resulting Hilbert space can be decomposed into a physical and unphysical subspace, which are mutually orthogonal. The physical subspace in the continuum limit reproduces that of the continuum theory and we give numerical evidence that the correct probability distributions for momentum and energy are recovered.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141946070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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