Imaginary Domain Research Articles

Dynamic exchange correlation effects in the strongly coupled electron liquid

The first quasiexact path integral Monte Carlo (PIMC) investigation of the dynamic local field correction G̃(q,zl;rs,Θ) in the imaginary Matsubara frequency domain is reported, focusing on the unpolarized uniform electron gas in the warm dense matter and strongly coupled regimes. The impact of dynamic exchange–correlation effects on the static structure factor is investigated. A straightforward explanation is provided for previously reported spurious effects in the so-called [Dornheim , ], where the frequency dependence of the local field correction is neglected. The comprehensive analysis of the asymptotic Matsubara order behavior, the density dependence, and the temperature dependence hints at the intriguing possibility of constructing an analytical four-parameter representation of G̃(q,zl;rs,Θ) valid for a substantial part of the uniform electron gas phase diagram, which would constitute key input for thermal density functional theory simulations. Published by the American Physical Society 2024

First-order localization and quantum phase transition induced by quasicrystal imaginary domain

The non-Hermitian extension of quasicrystals provides a highly tunable system for exploring novel material phases. While extended-localized phase transitions have been observed in one dimension, quantum phase transitions in higher dimensions and various system sizes remain unexplored. Here, we show the discovery of a new critical phase and first-order structural transition induced by imaginary zeros in the two-dimensional Haldane model with a quasicrystal potential on the upper boundary. Initially, we illustrate a phase diagram that evolves with the amplitude and phase of the quasicrystal potential, which is divided into three distinct phases by two critical boundaries: phase (I) with extended wave functions, parity-time-restore phase (II) with localized wave functions, and a critical phase (III) with multifunctional wave functions. To characterize the wave functions in these distinct phases, we introduce a low-energy approximation theory and an effective two-chain model. Additionally, we uncover a first-order quantum phase transition induced by quasicrystal domains. As we increase the size of the potential boundary, we observe the partitioning of the critical phase into regions in proportion to the growing number of quasicrystal domains. Importantly, these observations are consistent with ground state fidelity and energy gap calculations. Our research advances the understanding of phase diagrams associated with high-dimensional quasicrystal potentials and marks the first discovery of a first-order quantum phase transition induced by quasicrystal domains in non-Hermitian systems. Published by the American Physical Society 2024

Hermitian and pseudo-Hermitian Hamiltonians of [formula omitted] system—Spectrum, exceptional point, quantum–classical correspondence

We in this paper study the relation of hermiticity and energy spectrum for Hamiltonians consisting of SU(1,1) generators. In contrast with the common belief, the transition from real to imaginary spectra can appear at an exceptional point for the Hermitian Hamiltonian of a conservative system. The imaginary domain of spectrum resulted from an inverted potential well unbounded from below. An outward force applies on the particle, which moves acceleratingly away from the central point similar to the minisuperspace model of expanding universe. The Hamiltonian remains Hermitian beyond the exceptional point in a price that the boson-operator realization of SU(1,1) generator Ŝz becomes non-Hermitian. Oppositely a non-Hermitian Hamiltonian (called pseudo-Hermitian) possesses real eigenvalues in the entire region of interaction constant, which increases the gradient of potential well. While the Hermitian interaction decreases the gradient continuously to zero, namely the exceptional point, where eigenstates are degenerate. We extend the non-Hermitian Hamiltonian to the periodically time-dependent and two-dimensional system. The probability density of wave function coincides with classical orbits, which are derived from the corresponding classical-counterpart of the non-Hermitian quantum Hamiltonian.

Physical insights from imaginary-time density–density correlation functions

An accurate theoretical description of the dynamic properties of correlated quantum many-body systems, such as the dynamic structure factor S(q, ω), is important in many fields. Unfortunately, highly accurate quantum Monte Carlo methods are usually restricted to the imaginary time domain, and the analytic continuation of the imaginary-time density–density correlation function F(q, τ) to real frequencies is a notoriously hard problem. Here, it is argued that often no such analytic continuation is required because by definition, F(q, τ) contains the same physical information as does S(q, ω), only represented unfamiliarly. Specifically, it is shown how one can directly extract key information such as the temperature or quasi-particle excitation energies from the τ domain, which is highly relevant for equation-of-state measurements of matter under extreme conditions [T. Dornheim et al., Nat. Commun. 13, 7911 (2022)]. As a practical example, ab initio path-integral Monte Carlo results for the uniform electron gas (UEG) are considered, and it is shown that even nontrivial processes such as the roton feature of the UEG at low density [T. Dornheim et al., Commun. Phys. 5, 304 (2022)] are manifested straightforwardly in F(q, τ). A comprehensive overview is given of various useful properties of F(q, τ) and how it relates to the usual dynamic structure factor. In fact, working directly in the τ domain is advantageous for many reasons and opens up multiple avenues for future applications.

Low-rank Green's function representations applied to dynamical mean-field theory

Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In particular, the intermediate representation with sparse sampling and the discrete Lehmann representation (DLR) make use of low rank compression techniques to obtain optimal approximations with controllable accuracy. We consider the use of the DLR in dynamical mean-field theory (DMFT) calculations, and in particular show that the standard full Matsubara frequency grid can be replaced by the compact grid of DLR Matsubara frequency nodes. We test the performance of the method for a DMFT calculation of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ at temperature $50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ using a continuous-time quantum Monte Carlo impurity solver, and demonstrate that Matsubara frequency quantities can be represented on a grid of only 36 nodes with no reduction in accuracy, or increase in the number of self-consistent iterations, despite the presence of significant Monte Carlo noise.

Beyond Corporeal Constructs

The article is a brief analysis of Cornell’s Imaginary Domain (1995) as an intervention into decolonizing intersecting systems of oppression. Cornell’s Imaginary Domain forces us to think of the intersecting factors that retain systems of power. It isn’t just about one form of oppression but all systems of oppression that separate us. However, creating a shared struggle to find and embody wholeness in response to the historical traumas of slavery, segregation, and systems of anti-Black oppression is fraught with tensions.

The Political Imaginary, or the Democratic Transformation Domain

Abstract Cornelius Castoriadis’ entire work is shot through with reflections on the political imaginary, but it is rarely named explicitly and is not considered as a central, stand-alone, privileged idea within the social imaginary. This is why it is important to develop this idea in the domain of philosophy of politics. Moreover, for each contemporary democratic movement it is crucial to understand what “Political Imaginary” exactly is, to develop an effective change in politics in itself, as some Latin American countries (Brazil, Colombia and Chile) show us. In these countries, there are contemporary socio-historical examples of what is an effective transformation in the political imaginary domain. They allow us to enrich the meta-theoretical reflection through the historical identification of the political imaginary carried out by peculiar instituting movements that generated important transformations in the social self-representation and in the practice of collective power in the countries where they took place.

GENDER MAINSTREAMING – AN ETHICAL FEMINIST CONSIDERATION

In this article I tentatively consider the notion of gender mainstreaming from an ethical feminist perspective. Underlying this is a tension, or paradox, between law's limits and law's potential, law's poetry, poetry's law. A few theoretical arguments come into play. Firstly, the multiple meanings of sex and gender are reconsidered. Thereafter feminist critiques against the notion of one feminist method as well as a feminist jurisprudence are combined with a critical perspective on the institutionalisation of human rights and the politics of law. I recall these arguments to inform my investigation into gender mainstreaming. Two aspects are considered: firstly, in light of the critical perspectives, the preference for gender mainstreaming instead of challenging from the margins; and secondly, how mainstreaming actually takes place. Relying on the notion of ethical feminism and concepts of “asymmetrical reciprocity”, “city life”, the “imaginary domain” and the “community of the ought to be”, I ponder ways of making gender issues noticed beyond and within attempts at mainstreaming.

Scheming the Political Landscape: A New Communist Domain

The paper analyses and interprets Western radical left-wing scholars’ view on communism from the three dimensions of Ego, Other and the World in the modern philosophical context. The purpose of the research is to compare and reconstruct the three scientific categories of relations represented by communism, namely, the logical dialectical relations of Ego domain, Other domain and the World domain. The theoretical reconstruction and contextual analysis of Jacques Lacan and Sigmund Freud’s psychoanalysis, as well as numerous researchers of their work are used. The methodological basis of this research is a philosophical reconstruction and deductive speculation, inductive speculation and insight speculation approach. It is shown that the radical left scholars reexamine the evolution of communism from three basic categories: imaginary domain, symbolic domain and real domain. Furthermore, they reconsider the construction of communism through the study of the interrelations among Ego, Other and the World. Simultaneously, they also excavate the structural contradiction of contemporary capitalism and criticise its deficiencies. The weaknesses of the argument about these relations are shown by reconstructing this upward spiral relations, which can be considered an ideal model of domain structure in ‘The Neo-Communist domain’. On the basis of this claim, it is shown that these three types of domain structures may well coexist at least in ideal society, thus mankind should adhere to Marx’s dialectical materialism to consider problems. The scientific significance of the research is justifying that the philosophical reconstruction does not only enrich Marxist communist ideology and is of great practical significance for Socialist countries to reshape the ideals and beliefs of Marxism, but also stick to the development of Marxism and to expand the research horizon of communism. Nevertheless, the communist thought of western radical left scholars still has the dilemma of separating theory from practice and failing to transform theoretical communism into combatant communism.

Tearing energy calculation in hyperelastic fracture mechanics using the local and global complex-variable finite element method

The “local” and “global” complex-variable finite element methods were extended for computing the energy release rate (ERR) of materials undergoing nonlinear elastic deformation at both small and large strains. These methods compute the derivative of the strain energy with respect to crack length by applying a virtual crack extension through the imaginary domain of complex variables. The “global” complex finite element method (G-ZFEM) is a general sensitivity method that provides accurate ERR estimates regardless of the material and loading conditions in the cracked body. However, as G-ZFEM duplicates all the degrees of freedom of a finite element model to store information pertinent to the ERR, this analysis adds significant computational overhead. Local-based methods, analogous to the J-integral, can be employed to improve the computational efficiency of the fracture analysis. The “local” complex-variable finite element method (L-ZFEM) is a fracture-specific approach where complex-valued calculations are only conducted at a small group of elements surrounding the crack tip, adding minimum overhead to the analysis. The G-ZFEM and L-ZFEM methods were incorporated within the commercial finite element software ABAQUS through a two-dimensional user element that was linked to several material models, including Ramberg–Osgood, Neo-Hookean, and Mooney–Rivlin. The ERR, known as tearing energy (TE) in hyperelastic fracture problems, was obtained by the proposed methods in benchmark problems and found to be in excellent agreement with analytical formulations and the J-integral results. Unlike L-ZFEM and the J-integral, the G-ZFEM method does not exhibit variations in TE estimates with respect to the size or direction of the virtual crack extension in nonhomogeneous cracked bodies; thus, G-ZFEM estimates can be regarded as the reference tearing energy solutions. In addition, by using multidual or multicomplex algebra, the complex finite element methods allow the computation of arbitrary, higher-order derivatives of the strain energy with respect to the model’s material, loading, or geometric properties, providing additional information to design structural components with maximum resistance to fracture. The complex-variable methods are versatile and can be easily adapted to any nonlinear elastic material formulation and extended to 3D in a straightforward manner.

Thermodynamic Parameters of Central Spin Coupled to an Antiferromagnetic Bath: Path Integral Formalism

A path-integral representation of central spin system immersed in an antiferromagnetic environment was investigated. To carry out this study, we made use of the discrete-time propagator method associated with a basic set involving coherent states of Grassmann variables which made it possible to obtain the analytical propagator which is the centerpiece of the study. In this study, we considered that the environment was in the low-temperature and low-excitation limit and was split into 2 subnets that do not interact with each other. The evaluation of our system was made by considering the first neighbor approximation. From the formalism of the path integrals, it is easy to evaluate the partition function and thermodynamic properties followed from an appropriate tracing over Grassmann variables in the imaginary time domain. We show that the energy of the system depends on the number of sites n when β → 0.

Signatures of complex optical response in Casimir interactions of type I and II Weyl semimetals

The Casimir interaction, induced by electromagnetic fluctuations between objects, is strongly dependent upon the electronic and optical properties of the materials making up the objects. Here we investigate this ubiquitous interaction between semi-infinite spaces of topologically nontrivial Weyl semimetals. A comprehensive examination of all components of the bulk conductivity tensor and the surface conductivity due to the Fermi arc states in real and imaginary frequency domains is presented using the Kubo formalism for materials with different degree of tilting of their linear energy cones. The Casimir energy is calculated using a generalized Lifshitz approach, for which electromagnetic boundary conditions for anisotropic materials were derived and used. We find that the interaction between Weyl semimetals is metallic-like and its magnitude and characteristic distance dependence can be modified by the degree of tilting and chemical potential. The nontrivial topology plays a secondary role in the interaction and thermal fluctuations are expected to have similar effects as in metallic systems.

Empathy for Post-Abortion Grief in Louise Lambrichs's Journal d'Hannah (1993)

If abortion as a reproductive experience continues to retain a certain 'unspeakability' that keeps it on the margins of culture, the expression of grief or mourning in its wake remains even more inexpressible; to voluntarily terminate a pregnancy, no matter how fraught the circumstances, would seem to require the forfeiture of a right to acknowledge any resulting psychic loss. In her 1993 novel Journal d'Hannah, Louise Lambrichs gives us the 'diary' of a woman whose late-term abortion during WWII results in sterility. In mourning, Hannah creates an interior dream world in her diary in which her aborted daughter grows up in real time, as she remains unable to vocalize the pain of her loss to the exterior world. In this article, I explore the novel's capacity to push our understanding of what kinds of 'parental' mourning are acceptable and representable, and the ways in which the narrative confronts the lack of a broader cultural language with which to address this specific kind of grief.<br/> This article grounds its examination of Hannah's interiorized grief in theoretical notions of the unspeakability of trauma and feminist definitions of bodily integrity in the imaginary domain. I situate Lambrichs's work not as an anti-feminist indictment of abortion, as some have understood it, but as a challenge to open up a discursive space that enables an empathetic understanding of the diverse ways in which women deal with the voluntary termination of a pregnancy. Drawing on Barbara Johnson's (1986) exploration of the poetics of loss and abortion, I argue that the vocalization of post-abortion mourning need not result in the conclusion that taking 'the woman's feelings of guilt and loss into consideration... is to deny the right to choose the act that produced them' (33). The novel does not 'resolve' the tension of the confusing liminal space between life and death that abortion creates, but rather works to confront this liminality head on in a way that serves to question the limits of the ethics of parental mourning.

Dynamical BCS Theory of a Two-Dimensional Attractive Fermi Gas: Effective Interactions from Quantum Monte Carlo Calculations

The primary work presented in this paper focuses on the calculation of density-density dynamical correlations in an attractive two dimensional Fermi gas in several physically interesting regimes, including the strongly correlated BEC-BCS crossover regime. We use state-of-the-art dynamical BCS theory and we address the possibility to renormalize the interaction strength, using unbiased Quantum Monte Carlo results as an asset to validate the predictions. We propose that a suitable interplay between dynamical BCS theory, which is computationally very cheap and yields results directly in real time domain, and Quantum Monte Carlo methods, which are exact but way more demanding and limited to imaginary time domain, can be a very promising idea to study dynamics in many body systems. We illustrate the idea and provide quantitative results for a few values of the interaction strength in the cold gas.

Hamlet (RSC, 2016) and representations of diasporic blackness

In 2016 Paapa Essiedu, a British actor of Ghanaian ancestry, starred as Hamlet in Simon Godwin’s lauded Royal Shakespeare Company (RSC) production, set in a post-colonial African state whose non-specificity nonetheless irritated some reviewers. We contend, however, that the production mixed multiple referents of blackness (Eastern African, West African, Caribbean, South African, 1970s African American) in order deliberately to create an imaginary post-colonial domain where these different kinds of diasporic blackness engaged with each other through the figure of Hamlet and his art. We therefore examine how the concept of race changes with the transatlantic or transnational movement among spaces in this production.

Generalized rb Sets for Real and Imaginary Domains

Generalized rb Sets for Real and Imaginary Domains

Finite Temperature Coupled Cluster Theories for Extended Systems.

At zero temperature, coupled cluster theories are widely used to predict total energies, ground state expectation values, and even excited states for molecules and extended systems. However, for systems with a small band gap, such as metals, the zero-temperature approximation does not necessarily hold. Thermal effects may even give rise to interesting chemistry on metal surfaces. Most approaches to temperature dependent electronic properties employ finite temperature perturbation theory in the Matsubara frequency formulation. Computations require a large number of Matsubara frequencies to yield sufficiently accurate results, especially at low temperatures. This work, and independently the work of White and Chan J. Chem. Theory Comput. 2018 , DOI: 10.1021/acs.jctc.8b00773 , proposes a coupled cluster implementation directly in the imaginary time domain on the compact interval [0, β], closely related to the thermal cluster cumulant approach of Sanyal et al. [ Chem. Phys. Lett. 1992 , 192 , 55 - 61 ] , Sanyal et al. [ Phys. Rev. E 1993 , 48 , 3373 - 3389 ], and Mandal et al. [ Int. J. Mod. Phys. B 2003 , 17 , 5367 - 5377 ]. Here, the arising imaginary time dependent coupled cluster amplitude integral equations are solved in the linearized direct ring doubles approximation, also referred to as Tamm-Dancoff approximation with second order (linearized) screened exchange. In this framework, the transition from finite to zero temperature is uniform and comes at no extra costs, allowing to go to temperatures as low as room temperature. In this approximation, correlation grand potentials are calculated over a wide range of temperatures for solid lithium, a metallic system, and for solid silicon, a semiconductor.

A Novel Method of Signal Fusion Based on Dimension Expansion

A novel method of signal fusion, namely multi-dimensional unified signal (MDUS) fusion algorithm, is proposed based on dimensionality expansion of the cognitive radio (CR). The paper focuses on the issue of under-utilized and overcrowded spectrum bands in CR, through multi-component signal fusion. The proposed MDUS fusion algorithm can meet the basic requirement of signal fusion, that is, transmitting multi-component signal in one signal simultaneously, while basic signal elements, such as amplitude and bit rate, are not constrained by the fusion. The one-dimensional imaginary domain of the signal can be expanded to two, three or higher-dimensional imaginary space by exploiting the property of logical recursion. The original data flows can be extended to three, four or higher dimensions according to functional demands. Thus, the complementary aims of mutually independent orthogonal space and multivariate signal transmission without interference, are achieved by fusing multiple uni-dimensional signals into a multi-dimensional signal. Hence, based on the electromagnetic environment, a more flexible solution can be provided for spectrum occupancy of CR users. Specifically, the number of Orthogonal Frequency Division Multiplexing (OFDM) sub-bands and MDUS dimension can be dynamically converted, based on the MDUS–OFDM structure. The proposed approach can be utilized to provide more accurate estimation and prediction of transmission quality for CR Networks. Simulation results show the MDUS offers both BER and dimensionality advantage compared to the OFDM. Additionally, single-dimensional spectrum patterns can be expanded to alterable multi-dimensional spectrum patterns owing to the flexibility of MDUS–OFDM structure.

The Curious Case of a Robot Doctor: “Human,” Labor and Expert Systems

While Amazon Mechanical Turk project refreshes the long-term dream of artificial intelligence by incorporating human beings into the automation of information circuits, it also calls attention to the role of technical platforms in reorganizing the division and mode of labor under the current information capitalism. This essay examines this transformed labor regime by outlining the discourses and imaginaries of Artificial Intelligence (AI) in late 1970s and 1980s China when expert systems—an artificial intelligence system designed to provide expert consultation in the absence of human experts—first appeared. I argue that these discourses and imaginaries surrounding expert systems were tied to the anticipation of a coming information society, and to the fetish of expert knowledge, and a shift from Mao’s class-based politics to a depoliticized realm of professionalism. Bringing together the material, technical development of AI, the intellectual discourse of Post-Mao 1980s, as well as the imaginary domain of science fiction, this essay rethinks the politics of the “human” in the social context of Post-Mao’s era.

ドゥルシラ・コーネルによる中絶権と「イマジナリーな領域」の可能性

ドゥルシラ・コーネルによる中絶権と「イマジナリーな領域」の可能性