Reciprocal Symmetry Research Articles

Quantum advantage of one-way squeezing in weak-force sensing

Cavity optomechanical (COM) sensors, featuring efficient light–motion couplings, have been widely used for ultrasensitive measurements of various physical quantities ranging from displacements to accelerations or weak forces. Previous works, however, have mainly focused on reciprocal COM systems. Here, we propose how to further improve the performance of quantum COM sensors by breaking reciprocal symmetry in purely quantum regime. Specifically, we consider a spinning COM resonator and show that by selectively driving it in opposite directions, highly nonreciprocal optical squeezing can emerge, which in turn provides an efficient way to surpass the standard quantum limit which is otherwise unattainable for the corresponding reciprocal devices. Our work confirms that breaking reciprocal symmetry, already achieved in diverse systems well beyond spinning systems, can serve as a new strategy to further enhance the abilities of advanced quantum sensors, for applications ranging from testing fundamental physical laws to practical quantum metrology.

Reciprocal Symmetry via Inverse Series Pairs

Reciprocal series are employed to systematically review convolution sums, orthogonality relations, recurrence relations and reciprocal formulae for several classical number sequences, such as binomial coefficients, Stirling numbers, Bernoulli numbers, and Euler numbers.

Dissipation-induced acoustic nonreciprocity

Linear acoustic transmission through a stationary elastic medium possesses Rayleigh reciprocal symmetry with respect to pressure produced by a source at point A(B) and measured at point B(A), pA(rB) = pB(rA). In ideal (inviscid) fluids, pressure plays the role of the scalar potential for velocity, v∼∇p. The Rayleigh reciprocity theorem is formulated for velocity potentials but not for their gradients. Any function of the absolute value of velocity, v(r), lacks reciprocal symmetry. In particular, acoustic intencity I = pv is not symmetric, IA(rB) ≠ IB(rA). Dynamics of ideal fluid is time-reversible, and lack of reciprocal symmetry is attributed to asymmetry in scattering. However, in a viscous environment dissipation breaks T symmetry making fluid dynamics irreversible. We report that acoustic transmission is not only irreversible but also becomes nonreciprocal due to different amount of dissipated energy for forward and backward propagation, provided that mirror symmetry (P symmetry) is broken. Since dissipation occurs within a narrow viscous layer at solid–fluid interface, the amount of nonreciprocity in transmission strongly depends on the quality of the surface of scatterers. Experiments performed with scatterers of different surface quality show how surface roughness affects the level of nonreciprocity. In a series of experiments with asymmetric phononic crystal, Tesla valve, and acoustic cavity, we demonstrate dissipation-induced nonreciprocity in transmission. [This work is supported by the NSF under EFRI Grant No. 1741677.]

Using the Thermal Ratchet Mechanism to Achieve Net Motility in Magnetic Microswimmers.

Thermal ratchets can extract useful work from random fluctuations. This is common in the molecular scale, such as motor proteins, and has also been used to achieve directional transport in microfluidic devices. In this Letter, we use the ratchet principle to induce net motility in an externally powered magnetic colloid, which otherwise shows reciprocal (back and forth) motion. The experimental system is based on ferromagnetic micro helices driven by oscillating magnetic fields, where the reciprocal symmetry is broken through asymmetric actuation timescales. The swimmers show net motility with an enhanced diffusivity, in agreement with the numerical calculations. This new class of microscale, magnetically powered, active colloids can provide a promising experimental platform to simulate diverse active matter phenomena in the natural world.

An uncertainty-induced axiomatic foundation of the analytic hierarchy process and its implication

Uncertainty is always encountered by decision makers (DMs) when addressing a complex decision-making problem. The existing axiomatic foundation of the analytic hierarchy process (AHP) cannot reflect the uncertainty experienced by DMs. In this paper, it is first to find that the uncertainty experienced by DMs can be characterized by the non-reciprocal property of pairwise comparisons. The novel concept of reciprocal symmetry breaking (RSB) is proposed to capture the situation without reciprocal property. Then an uncertainty-induced axiomatic foundation of the AHP model is reported, where the RSB is one of the proposed axioms. Some interesting results are derived from the new axioms involving the concept of approximate consistency and the method of eliciting priorities. An index is constructed to measure approximate consistency degree of pairwise comparison matrices (PCMs). Some comparisons with the typical AHP model are offered by carrying out some numerical examples. The obtained results reveal that the proposed axiomatic foundation and the derived facts form a novel operational basis of the AHP model under uncertainty.

Multiplicity of Radial Ground States for the Scalar Curvature Equation Without Reciprocal Symmetry

We study existence and multiplicity of positive ground states for the scalar curvature equation Δu+K(|x|)un+2n-2=0,x∈Rn,n>2,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\varDelta u+ K(|x|)\\, u^{\\frac{n+2}{n-2}}=0, \\quad x\\in {{\\mathbb {R}}}^n\\,, \\quad n>2, \\end{aligned}$$\\end{document}when the function K:{{mathbb {R}}}^+rightarrow {{mathbb {R}}}^+ is bounded above and below by two positive constants, i.e. 0<underline{K} le K(r) le overline{K} for every r > 0, it is decreasing in (0,{{{mathcal {R}}}}) and increasing in ({{{mathcal {R}}}},+infty ) for a certain {{{mathcal {R}}}}>0. We recall that in this case ground states have to be radial, so the problem is reduced to an ODE and, then, to a dynamical system via Fowler transformation. We provide a smallness non perturbative (i.e. computable) condition on the ratio overline{K}/underline{K} which guarantees the existence of a large number of ground states with fast decay, i.e. such that u(|x|) sim |x|^{2-n} as |x| rightarrow +infty , which are of bubble-tower type. We emphasize that if K(r) has a unique critical point and it is a maximum the radial ground state with fast decay, if it exists, is unique.

Characteristic Mueller matrices for direct assessment of the breaking of symmetries.

Mueller polarimetry is a powerful optical technique in the analysis of micro-structural properties of optical samples. However, there is no explicit relationship between individual Mueller matrix elements and the physical properties of the sample. Several matrix decomposition algorithms corresponding to specific optical models have been proposed, which extract the physical information from measured Mueller matrices. Nevertheless, we still need a prior assessment method to decide which model is more suitable for the experimental data. In this Letter, we propose a set of characteristic Mueller matrices that allows us to obtain information about the breaking of rotation, mirror, and reciprocal symmetry properties in the sample by direct inspection of several elements of the Mueller matrix. By further analyzing the possible origin of symmetry breaking, we can learn the type and mixing status of anisotropies in the measured sample. We have verified our theory with Monte Carlo simulations of polarized light scattering in an isotropic or anisotropic medium containing different configurations of spherical and cylindrical scatterers. This study may help experimenters choose more suitable Mueller matrix decomposition methods.

Non-reciprocal wave phenomena in energy self-reliant gyric metamaterials.

This work presents a mechanism by which non-reciprocal wave transmission is achieved in a class of gyric metamaterial lattices with embedded rotating elements. A modulation of the device's angular momentum is obtained via prescribed rotations of a set of locally housed spinning motors and is then used to induce space-periodic, time-periodic, as well as space-time-periodic variations, which influence wave propagation in distinct ways. Owing to their dependence on gyroscopic effects, such systems are able to break reciprocal wave symmetry without stiffness perturbations rendering them consistently stable as well as energy self-reliant. Dispersion patterns, band gap emergence, as well as non-reciprocal wave transmission in the space-time-periodic gyric metamaterials are predicted both analytically from the gyroscopic system dynamics as well as numerically via time-dependent full wave simulations. In addition to breaking reciprocity, the authors show that the energy content of a frictionless gyric metamaterial is conserved over one temporal modulation cycle enabling it to exhibit a stable response irrespective of the pumping frequency.

Circulators at the Quantum Limit: Recent Realizations of Quantum-Limited Superconducting Circulators and Related Approaches

A well-known component of RF systems is the circulator, a three-port device that allows signals to flow in one direction while inhibiting propagation in the reverse direction. Circulators play an important role in protecting sensitive RF devices from reflections and are used to isolate the transmitter from the receiver chains in monostatic radar architectures. Circulators are also fascinating on their own, providing a textbook example of how reciprocal symmetry is broken. This symmetry-the invariance of device transmission under the exchange of sources and detectors-is a very common property that applies to most passive microwave devices. For example, antenna gain does not change whether the antenna is used as a transmitter or a receiver. Likewise, attenuator loss does not depend on the attenuator's orientation.

Microdisplays as a versatile tool for the optical simulation of crystal diffraction in the classroom

Presented here is a flexible and low-cost setup for demonstrating X-ray, electron or neutron diffraction methods in the classroom. Using programmable spatial light modulators extracted from a commercial video projector, physical diffraction patterns are generated, in real time, of any two-dimensional structure which can be displayed on a computer screen. This concept enables hands-on experience beyond simplest-case scenarios of scattering phenomena, and for the students, the transfer to the regime of visible light greatly enhances intuitive understanding of diffraction in real and reciprocal space. The idea and working principle of the modified video projector are explained, technical advice is given for its choice and successful modification, and a Python-based open-source program code is provided. Program features include the design and interactive manipulation of two-dimensional crystal structures to allow a straightforward demonstration of concepts such as reciprocal space, structure factors, selection rules, symmetry and symmetry violation, as well as structural disorder. This approach has already proved helpful in teaching crystal diffraction to undergraduate students in materials science.

The Impact of AI and Reciprocal Symmetry on Organizational Culture and Leadership in the Digital Economy

The profound effects of reciprocal symmetry and artificial intelligence (AI) on leadership and organizational culture in the digital economy are examined in this study. Examining the impact of AI and reciprocal symmetry integration on leadership styles, workplace ethics, and organizational dynamics are among the main goals. Using a secondary data-based review process, the study synthesizes current literature, research papers, and empirical findings relevant to AI adoption and reciprocal symmetry principles in corporate environments. Significant findings show that AI technologies transform organizational culture, resulting in cultural shifts toward data-driven decision-making, innovation, and cooperation. Principles of reciprocal symmetry promote inclusive environments that highly value openness, justice, and respect for all parties involved. Ethical questions become increasingly important with policy ramifications that demand regulatory frameworks and moral norms to ensure responsible AI deployment and conformity with societal values. This study emphasizes ethical involvement, adaptive leadership, and teamwork when utilizing AI and reciprocal symmetry to promote favorable organizational and social outcomes in the digital economy. Organizations can manage AI adoption while promoting human-centric cultures and long-term value generation by adopting reciprocal symmetry principles.

Artificial Intelligence, Reciprocal Symmetry, and Customer Relationship Management: A Paradigm Shift in Business

This article examines how combining reciprocal symmetry, artificial intelligence (AI), and customer relationship management (CRM) might change corporate paradigms and promote long-term growth. Investigating the convergence of AI and reciprocal symmetry principles within CRM, examining AI's role in fostering customer-centric relationships, and identifying policy implications for responsible AI use in business practices are the main goals of this study. This study's methodology uses a secondary data-based review strategy to synthesize industry reports, academic publications, and current literature to analyze the conceptual framework and real-world applications of AI-driven CRM tactics integrated with the concepts of reciprocal symmetry. Important discoveries show that combining reciprocal symmetry and AI improves personalization, encourages team-based innovation, and puts customers' needs first in CRM. However, to guarantee safe AI adoption in commercial contexts, issues like data privacy consequences and ethical considerations highlight the necessity for explicit regulations and guidelines. The policy implications underscore the significance of formulating legislation that protects consumer rights, encourages ethical AI implementation, and sets benchmarks for AI-powered CRM procedures. The study highlights the potential of artificial intelligence (AI) and reciprocal symmetry to drive a paradigm shift in corporate relationships and innovation towards a customer-centric approach.

Analyzing power-thermal-performance trade-offs in a high-performance 3D NoC architecture

The emergence of three-dimensional (3D) network-on-chip (NoC) has revolutionized the design of high-performance and energy efficient manycore chips. However, in general, 3D NoC architectures still suffer from high power density and the resultant thermal hotspots leading to functionality and reliability concerns over time. The power consumption and thermal profiles of 3D NoCs can be improved by incorporating a Voltage Frequency Island (VFI)-based power management strategy and Reciprocal Design Symmetry (RDS)-based floor planning. In this paper, we undertake a detailed design space exploration for 3D NoC by considering power-thermal-performance (PTP) trade-offs. We specifically consider a small-world network-enabled 3D NoC (3D SWNoC) in this performance evaluation due to its superior performance and energy-efficiency compared to any other existing 3D NoC architectures. We demonstrate that the VFI-enabled 3D SWNoC lowers the energy-delay-product (EDP) by 57.3% on an average compared to a 2D MESH without VFI. Moreover, by incorporating VFI, we reduce the maximum temperature of 3D SWNoC by 15.2% on an average compared to the non-VFI counterpart. By complementing the VFI-based power management with RDS-based floor planning, the 3D SWNoC reduces the maximum temperature by 25.1% on an average compared to the non-VFI counterpart.

Nonequilibrium work relation from Schrödinger’s unrecognized probability theory

Jarzynski’s nonequilibrium work relation can be understood as the realization of the (hidden) time-generator reciprocal symmetry satisfied for the conditional probability function. To show this, we introduce the reciprocal process where the classical probability theory is expressed with real wave functions, and derive a mathematical relation using the symmetry. We further discuss that the descriptions by the standard Markov process from an initial equilibrium state are indistinguishable from those by the reciprocal process. Then the Jarzynski relation is obtained from the mathematical relation for the Markov processes described by the Fokker–Planck, Kramers and relativistic Kramers equations.

Managing Digital Transformation: The Role of Artificial Intelligence and Reciprocal Symmetry in Business

This study aims to understand better how corporate organizations may manage digital transformation by utilizing reciprocal symmetry and artificial intelligence (AI). The study aims to investigate the effects of artificial intelligence (AI) technologies on conventional business models, assess the possibilities and difficulties of attaining reciprocal symmetry in the context of digital transformation, and pinpoint methods for efficient AI integration that maintain organizational preparedness and alignment. Using a secondary data-based review methodology, the study synthesizes previous research on digital transformation, AI integration, organizational adaptation, and extant literature. Key conclusions show how crucial it is to have a culture of innovation, collaborate across functional boundaries, and plan strategically to maximize the advantages of digital transformation projects and achieve reciprocal symmetry. The policy implications underscore the necessity of allocating resources towards digital infrastructure, skills enhancement, and regulatory frameworks to facilitate the responsible adoption of AI and tackle obstacles such as limited resources, skills disparity, and cultural opposition. Organizations may handle technology upheavals and promote competitiveness and sustainable growth in the digital era by adopting reciprocal symmetry and supportive policies.

Wave physics of the graphene lattice emulated in a ripple tank

Using the example of graphene, we have extended the classic ripple tank experiment to illustrate the behavior of waves in periodic lattices. A loudspeaker driving air through a periodically perforated plate onto the tank's water surface creates wave patterns that are in agreement with numerical simulations and are explained in terms of solid state theory. From an educational point of view, the experiment provides an illustrative example of the concepts of reciprocal space and symmetry.

Un concettualista romantico

A reciprocal symmetry between art and culture, the reductionism and the impoverishment of the artistic practices are all consequences of the establishment of the new conceptualist paradigm in art since the 60s. Nespolo’s artistic production in that period exemplifies this features being thus conceivable as a variant of conceptualism since he adopts its new experimental rules mixing them with the traditional ones of the visual artistic paradigm.

Anisotropic particle in viscous shear flow: Navier slip, reciprocal symmetry, and Jeffery orbit.

The hydrodynamic reciprocal theorem for Stokes flows is generalized to incorporate the Navier slip boundary condition, which can be derived from Onsager's variational principle of least energy dissipation. The hydrodynamic reciprocal relations and the Jeffery orbit, both of which arise from the motion of a slippery anisotropic particle in a simple viscous shear flow, are investigated theoretically and numerically using the fluid particle dynamics method [Phys. Rev. Lett. 85, 1338 (2000)]. For a slippery elliptical particle in a linear shear flow, the hydrodynamic reciprocal relations between the rotational torque and the shear stress are studied and related to the Jeffery orbit, showing that the boundary slip can effectively enhance the anisotropy of the particle. Physically, by replacing the no-slip boundary condition with the Navier slip condition at the particle surface, the cross coupling between the rotational torque and the shear stress is enhanced, as manifested through a dimensionless parameter in both of the hydrodynamic reciprocal relations and the Jeffery orbit. In addition, simulations for a circular particle patterned with portions of no-slip and Navier slip are carried out, showing that the particle possesses an effective anisotropy and follows the Jeffery orbit as well. This effective anisotropy can be tuned by changing the ratio of no-slip portion to slip potion. The connection of the present work to nematic liquid crystals' constitutive relations is discussed.

A Variational approach to thin film hydrodynamics of binary mixtures

In order to model the dynamics of thin films of mixtures, solutions, and suspensions, a thermodynamically consistent formulation is needed such that various coexisting dissipative processes with cross couplings can be correctly described in the presence of capillarity, wettability, and mixing effects. In the present work, we apply Onsager's variational principle to the formulation of thin film hydrodynamics for binary fluid mixtures. We first derive the dynamic equations in two spatial dimensions, one along the substrate and the other normal to the substrate. Then, using long-wave asymptotics, we derive the thin film equations in one spatial dimension along the substrate. This enables us to establish the connection between the present variational approach and the gradient dynamics formulation for thin films. It is shown that for the mobility matrix in the gradient dynamics description, Onsager's reciprocal symmetry is automatically preserved by the variational derivation. Furthermore, using local hydrodynamic variables, our variational approach is capable of introducing diffusive dissipation beyond the limit of dilute solute. Supplemented with a Flory–Huggins-type mixing free energy, our variational approach leads to a thin film model that treats solvent and solute in a symmetric manner. Our approach can be further generalized to include more complicated free energy and additional dissipative processes.

Elementary polarization properties in the backscattering configuration.

In the normal incidence backscattering configuration, a polarimetric measurement always preserves the reciprocal symmetry. For a reciprocal Jones matrix, the number of elementary polarization properties is reduced from six to four. In this work, the physical interpretation of these properties is examined and they are compared with the equivalent polarization properties in transmission. It is found that, with the exception of natural optical activity, a polarimetric backreflection experiment can essentially provide the same type of information about the anisotropy of a medium as a transmission analysis, although transmission and backreflection information comes in a completely different form. Experimental examples are provided to illustrate the discussion.