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Journal articles on the topic 'Heisenberg limit'

Author: Grafiati

Published: 25 May 2024

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1

Gaete, Patricio. "Some Remarks on Nonlinear Electrodynamics." Advances in High Energy Physics 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/2463203.

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By using the gauge-invariant, but path-dependent, variables formalism, we study both massive Euler-Heisenberg-like and Euler-Heisenberg-like electrodynamics in the approximation of the strong-field limit. It is shown that massive Euler-Heisenberg-type electrodynamics displays the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy for both classes of electrodynamics. As a result, for the case of massive Euler-Heisenbeg-like electrodynamics (Wichmann-Kroll), unexpected features are found. We obtain a new long-range (1/r3-type) correction, apart from a long-range(1/r5-type) correction to the Coulomb potential. Furthermore, Euler-Heisenberg-like electrodynamics in the approximation of the strong-field limit (to the leading logarithmic order) displays a long-range (1/r5-type) correction to the Coulomb potential. Besides, for their noncommutative versions, the interaction energy is ultraviolet finite.

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2

Putra, Fima Ardianto. "De Broglie Wave Analysis of the Heisenberg Uncertainty Minimum Limit under the Lorentz Transformation." Jurnal Teras Fisika 1, no. 2 (September 20, 2018): 1. http://dx.doi.org/10.20884/1.jtf.2018.1.2.1008.

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A simple analysis using differential calculus has been done to consider the minimum limit of the Heisenberg uncertainty principle in the relativistic domain. An analysis is made by expressing the form of and based on the Lorentz transformation, and their corresponding relation according to the de Broglie wave packet modification. The result shows that in the relativistic domain, the minimum limit of the Heisenberg uncertainty is p x ?/2 and/or E t ?/2, with is the Lorentz factor which depend on the average/group velocity of relativistic de Broglie wave packet. While, the minimum limit according to p x ?/2 or E t ?/2, is the special case, which is consistent with Galilean transformation. The existence of the correction factor signifies the difference in the minimum limit of the Heisenberg uncertainty between relativistic and non-relativistic quantum. It is also shown in this work that the Heisenberg uncertainty principle is not invariant under the Lorentz transformation. The form p x ?/2 and/or E t ?/2 are properly obeyed by the Klein-Gordon and the Dirac solution. Key words: De Broglie wave packet, Heisenberg uncertainty, Lorentz transformation, and minimum limit.

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3

Luis, Alfredo. "Nonlinear transformations and the Heisenberg limit." Physics Letters A 329, no. 1-2 (August 2004): 8–13. http://dx.doi.org/10.1016/j.physleta.2004.06.080.

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4

SIOPSIS, GEORGE. "THE PENROSE LIMIT OF AdS×S SPACE AND HOLOGRAPHY." Modern Physics Letters A 19, no. 12 (April 20, 2004): 887–95. http://dx.doi.org/10.1142/s0217732304013891.

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In the Penrose limit, AdS ×S space turns into a Cahen–Wallach (CW) space whose Killing vectors satisfy a Heisenberg algebra. This algebra is mapped onto the holographic screen on the boundary of AdS. We show that the Heisenberg algebra on the boundary of AdS may be obtained directly from the CW space by appropriately constraining the states defined on it. The transformations generated by the constraint are similar to gauge transformations. The "holographic screen" on the CW space is thus obtained as a "gauge-fixing" condition.

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5

Sanchidrián-Vaca, Carlos, and Carlos Sabín. "Parameter Estimation of Wormholes beyond the Heisenberg Limit." Universe 4, no. 11 (November 6, 2018): 115. http://dx.doi.org/10.3390/universe4110115.

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We propose to exploit the quantum properties of nonlinear media to estimate the parameters of massless wormholes. The spacetime curvature produces a change in length with respect to Minkowski spacetime that can be estimated in principle with an interferometer. We use quantum metrology techniques to show that the sensitivity is improved with nonlinear media and propose a nonlinear Mach–Zehnder interferometer to estimate the parameters of massless wormholes that scales beyond the Heisenberg limit.

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6

Napolitano, M., M. Koschorreck, B. Dubost, N. Behbood, R. J. Sewell, and M. W. Mitchell. "Quantum Optics and the “Heisenberg Limit” of Measurement." Optics and Photonics News 22, no. 12 (December 1, 2011): 40. http://dx.doi.org/10.1364/opn.22.12.000040.

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7

Ohring, Peter. "A central limit theorem on Heisenberg type groups." Proceedings of the American Mathematical Society 113, no. 2 (February 1, 1991): 529. http://dx.doi.org/10.1090/s0002-9939-1991-1045146-7.

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8

Maleki, Yusef, and Aleksei M. Zheltikov. "Spin cat-state family for Heisenberg-limit metrology." Journal of the Optical Society of America B 37, no. 4 (March 10, 2020): 1021. http://dx.doi.org/10.1364/josab.374221.

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9

Unternährer, Manuel, Bänz Bessire, Leonardo Gasparini, Matteo Perenzoni, and André Stefanov. "Super-resolution quantum imaging at the Heisenberg limit." Optica 5, no. 9 (September 20, 2018): 1150. http://dx.doi.org/10.1364/optica.5.001150.

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10

TSVELIK, A. M. "TWO WEAKLY COUPLED HEISENBERG CHAINS—SOLUTION IN CONTINUOUS LIMIT." Modern Physics Letters B 05, no. 30 (December 30, 1991): 1973–79. http://dx.doi.org/10.1142/s0217984991002379.

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Using the bosonization procedure proposed for the spin-1/2 Heisenberg chain in Ref. 8 we obtain the effective Hamiltonian for the system of two weakly coupled Heisenberg chains with the XXZ anisotropy as the sum of two sine-Gordon Hamiltonians. It appears that this simple system reveals a rather rich variety of properties in different regions of anisotropy. We calculate the spin-spin correlation functions; two-spin correlation functions decay exponentially but there are regions where the four-spin correlation functions decay as a power law. In particular, if both the inter- and intrachain exchange interactions are isotropic and the interchain exchange is ferromagnetic correlations of the chirality field χ= S 1× S 2 (the indexes 1 and 2 numerate the chains) are enhanced and their correlation functions follow a power law. In this case coupling between pairs of chains can lead to chiral ordering in three dimensions.

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11

Gietka, Karol, Friederike Metz, Tim Keller, and Jing Li. "Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied." Quantum 5 (July 1, 2021): 489. http://dx.doi.org/10.22331/q-2021-07-01-489.

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We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore regular quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-Zener model and the quantum Rabi model.

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12

Majumder, Arunava, Harshank Shrotriya, and Leong-Chuan Kwek. "Strategies for Positive Partial Transpose (PPT) States in Quantum Metrologies with Noise." Entropy 23, no. 6 (May 28, 2021): 685. http://dx.doi.org/10.3390/e23060685.

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Quantum metrology overcomes standard precision limits and has the potential to play a key role in quantum sensing. Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurements. Conventional bounds to the measurement precision such as the shot noise limit are not as fundamental as the Heisenberg limits, and can be beaten with quantum strategies that employ ‘quantum tricks’ such as squeezing and entanglement. Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered to be too weakly entangled for applications. Since no pure entanglement can be distilled from them, they are also called bound entangled states. We provide strategies, using which multipartite quantum states that have a positive partial transpose with respect to all bi-partitions of the particles can still outperform separable states in linear interferometers.

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13

Kowalski, Andres Mauricio, Angelo Plastino, and Gaspar Gonzalez. "Classical Limit, Quantum Border and Energy." Physics 5, no. 3 (July 26, 2023): 832–50. http://dx.doi.org/10.3390/physics5030053.

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We analyze the (dynamical) classic limit of a special semiclassical system. We describe the interaction of a quantum system with a classical one. This limit has been well studied before as a function of a constant of motion linked to the Heisenberg principle. In this paper, we investigate the existence of the mentioned limit, but with reference to the total energy of the system. Additionally, we find an attractive result regarding the border of the transition.

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14

VILLAIN-GUILLOT, SIMON, and ROSSEN DANDOLOFF. "COUPLING CONSTANT AND MAGNON VELOCITY FOR A TWO-DIMENSIONAL QUANTUM HEISENBERG ANTIFERROMAGNET: THE CONTINUUM LIMIT." Modern Physics Letters B 10, no. 28 (December 10, 1996): 1389–95. http://dx.doi.org/10.1142/s0217984996001565.

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We study Heisenberg spins on an infinite plane. Following an approach developed by Affleck, we find that the Heisenberg Hamiltonian is equivalent in the continuum limit to the nonlinear σ model. And we show that the auxiliary fields, which appear because of the conservation of the number of degrees of freedom, are related to the covariant derivatives of the order parameter. These auxiliary fields have to be taken into account in order to recover the expected values for the coupling constant and magnon velocity in two-dimensions.

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15

Hu, De Zhi. "Exploration of Hyperfine Micro-Machining Limit." Advanced Materials Research 941-944 (June 2014): 2145–48. http://dx.doi.org/10.4028/www.scientific.net/amr.941-944.2145.

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Combining the latest achievements of scientists to study cosmology, the machining accuracy of microelectronic devices is not the limit size of hyperfine micro-machining processing. In the future, it will develop a novel micro-machining method using dark energy and dark matter, and setup a new era. The paper introduces the Planck scale and the Heisenberg uncertainty relation into the Newtonian gravity for the model simplification. Newtonian gravity can be separated into two parts that is Dark Matter and Dark Energy. Every part is inverse relation to the distance.

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16

Stephan, W., and B. W. Southern. "Is there a phase transition in the isotropic Heisenberg anti-ferromagnet on the triangular lattice?" Canadian Journal of Physics 79, no. 11-12 (December 1, 2001): 1459–61. http://dx.doi.org/10.1139/p01-086.

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The phase diagram of the classical anisotropic (XXZ) Heisenberg model on the two-dimensional triangular lattice is investigated using Monte Carlo methods. In the easy-axis limit, two finite-temperature vortex-unbinding transitions have been observed. In the easy-plane limit, there also appear to be two distinct finite-temperature phase transitions that are very close in temperature. The upper transition corresponds to an Ising-like chirality ordering and the lower temperature transition corresponds to a KosterlitzThouless vortex-unbinding transition. These phase-transition lines all meet at the Heisenberg point and provide strong evidence that the isotropic model undergoes a novel finite-temperature phase transition. PACS Nos.: 75.10Hk, 75.40Mg

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17

Ohring, Peter. "A central limit theorem on Heisenberg type groups. II." Proceedings of the American Mathematical Society 118, no. 4 (April 1, 1993): 1313. http://dx.doi.org/10.1090/s0002-9939-1993-1137231-8.

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18

Steuernagel, Ole, and Stefan Scheel. "Approaching the Heisenberg limit with two-mode squeezed states." Journal of Optics B: Quantum and Semiclassical Optics 6, no. 3 (March 1, 2004): S66—S70. http://dx.doi.org/10.1088/1464-4266/6/3/011.

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19

Cao, Zhaozhong. "Uncertainty principle and complementary variables." Highlights in Science, Engineering and Technology 61 (July 30, 2023): 18–23. http://dx.doi.org/10.54097/hset.v61i.10260.

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The two most important areas in modern physics are quantum mechanics and the theory of relativity. Unlike classical physics, where Newton's mechanics dominates, these two areas change human beings' fundamental view of the universe. One of the theories that build up the base of quantum mechanics is Heisenberg's Uncertainty Principle. Starting from a thought experiment, Heisenberg's microscope in the setting of classical physics, Werner Heisenberg built a bridge between classical and quantum physics by presenting a counterintuitive outcome in the thought experiment. Since then, the observer of a physics phenomenon is no longer a bystander. The behavior of observation became a part of the physical experiment. To come up with a mathematical expression that can describe such a new discovery, Heisenberg came up with matrix mechanics and the concept of complementary variables. There is a trade-off between a pair of complementary variables. When one of them is measured precisely, meaning the information of that variable is known on a large scale, the other variable can not be measured precisely, meaning there is no way to know enough information about the other variable. The principle indicates a fundamental limit on what human beings can know about the unknown variables. The discoveries of other complementary variables help physicists know the new image of the physics world under new rules.

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20

FARACH, H. A., R. J. CRESWICK, and C. P. POOLE. "THE RESTRICTED SPIN MODEL." Modern Physics Letters B 04, no. 16 (September 10, 1990): 1029–41. http://dx.doi.org/10.1142/s0217984990001306.

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We present a novel anisotropic Heisenberg model in which the classical spin is restricted to a region of the unit sphere which depends on the value of the anisotropy parameter Δ. In the limit Δ→1, we recover the Ising model, and in the limit Δ→0, the isotopic Heisenberg model. Monte Carlo calculations are used to compare the critical temperature as a function of the anisotropy parameter for the restricted and unrestricted models, and finite-size scaling analysis leads to the conclusion that for all Δ>0 the model belongs to the Ising universality class. For small A the critical behavior is clearly seen in histograms of the transverse and longitudinal (z) components of the magnetization.

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21

Putra, Fima Ardianto. "On the Semiclassical Approach of the Heisenberg Uncertainty Relation in the Strong Gravitational Field of Static Blackhole." Jurnal Fisika Indonesia 22, no. 2 (April 16, 2020): 15. http://dx.doi.org/10.22146/jfi.v22i2.34274.

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Heisenberg Uncertainty and Equivalence Principle are the fundamental aspect respectively in Quantum Mechanic and General Relativity. Combination of these principles can be stated in the expression of Heisenberg uncertainty relation near the strong gravitational field i.e. pr and Et . While for the weak gravitational field, both relations revert to pr and Et. It means that globally, uncertanty principle does not invariant. This work also shows local stationary observation between two nearby points along the radial direction of blackhole. The result shows that the lower point has larger uncertainty limit than that of the upper point, i.e. . Hence locally, uncertainty principle does not invariant also. Through Equivalence Principle, we can see that gravitation can affect Heisenberg Uncertainty relation. This gives the impact to our’s viewpoint about quantum phenomena in the presence of gravitation. Key words: Heisenberg Uncertainty Principle , Equivalence Principle, and gravitational field

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22

Dutkiewicz, Alicja, Barbara M. Terhal, and Thomas E. O'Brien. "Heisenberg-limited quantum phase estimation of multiple eigenvalues with few control qubits." Quantum 6 (October 6, 2022): 830. http://dx.doi.org/10.22331/q-2022-10-06-830.

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Quantum phase estimation is a cornerstone in quantum algorithm design, allowing for the inference of eigenvalues of exponentially-large sparse matrices.The maximum rate at which these eigenvalues may be learned, –known as the Heisenberg limit–, is constrained by bounds on the circuit complexity required to simulate an arbitrary Hamiltonian. Single-control qubit variants of quantum phase estimation that do not require coherence between experiments have garnered interest in recent years due to lower circuit depth and minimal qubit overhead. In this work we show that these methods can achieve the Heisenberg limit, also when one is unable to prepare eigenstates of the system. Given a quantum subroutine which provides samples of a `phase function' g(k)=∑jAjeiϕjk with unknown eigenphases ϕj and overlaps Aj at quantum cost O(k), we show how to estimate the phases {ϕj} with (root-mean-square) error δ for total quantum cost T=O(δ−1). Our scheme combines the idea of Heisenberg-limited multi-order quantum phase estimation for a single eigenvalue phase [Higgins et al (2009) and Kimmel et al (2015)] with subroutines with so-called dense quantum phase estimation which uses classical processing via time-series analysis for the QEEP problem [Somma (2019)] or the matrix pencil method. For our algorithm which adaptively fixes the choice for k in g(k) we prove Heisenberg-limited scaling when we use the time-series/QEEP subroutine. We present numerical evidence that using the matrix pencil technique the algorithm can achieve Heisenberg-limited scaling as well.

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23

Rendon, Gumaro, Jacob Watkins, and Nathan Wiebe. "Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation." Quantum 8 (February 26, 2024): 1266. http://dx.doi.org/10.22331/q-2024-02-26-1266.

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Quantum metrology allows for measuring properties of a quantum system at the optimal Heisenberg limit. However, when the relevant quantum states are prepared using digital Hamiltonian simulation, the accrued algorithmic errors will cause deviations from this fundamental limit. In this work, we show how algorithmic errors due to Trotterized time evolution can be mitigated through the use of standard polynomial interpolation techniques. Our approach is to extrapolate to zero Trotter step size, akin to zero-noise extrapolation techniques for mitigating hardware errors. We perform a rigorous error analysis of the interpolation approach for estimating eigenvalues and time-evolved expectation values, and show that the Heisenberg limit is achieved up to polylogarithmic factors in the error. Our work suggests that accuracies approaching those of state-of-the-art simulation algorithms may be achieved using Trotter and classical resources alone for a number of relevant algorithmic tasks.

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24

Franceschi, Valentina, Francescopaolo Montefalcone, and Roberto Monti. "CMC Spheres in the Heisenberg Group." Analysis and Geometry in Metric Spaces 7, no. 1 (January 1, 2019): 109–29. http://dx.doi.org/10.1515/agms-2019-0006.

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Abstract We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group H1. These spheres are conjectured to be the isoperimetric sets of H1. We prove several results supporting this conjecture. We also focus our attention on the sub-Riemannian limit.

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25

Maiti, Debasmita, Dayasindhu Dey, and Manoranjan Kumar. "Study of Interacting Heisenberg Antiferromagnet Spin-1/2 and 1 Chains." Condensed Matter 8, no. 1 (January 29, 2023): 17. http://dx.doi.org/10.3390/condmat8010017.

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Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferromagnetic (HAF) of the spin S chain is that the half-integer and the integer S chain have gapless and gapped energy spectrums, respectively. The ground state (gs) of the HAF spin-1/2 and spin-1 chains have a quasi-long-range and short-range correlation, respectively. We study the effect of the exchange interaction between an HAF spin-1/2 and an HAF spin-1 chain forming a normal ladder system and its gs properties. The inter-chain exchange interaction J⊥ can be either ferromagnetic (FM) or antiferromagnetic (AFM). Using the density matrix renormalization group method, we show that in the weak AFM/FM coupling limit of J⊥, the system behaves like two decoupled chains. However, in the large AFM J⊥ limit, the whole system can be visualized as weakly coupled spin-1/2 and spin-1 pairs which behave like an effective spin-1/2 HAF chain. In the large FM J⊥ limit, coupled spin-1/2 and spin-1 pairs can form pseudo spin-3/2 and the whole system behaves like an effective spin-3/2 HAF chain. We also derive the effective model Hamiltonian in both strong FM and AFM rung exchange coupling limits.

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26

JANIŠ, V., and D. VOLLHARDT. "COMPREHENSIVE MEAN FIELD THEORY FOR THE HUBBARD MODEL." International Journal of Modern Physics B 06, no. 05n06 (March 1992): 731–47. http://dx.doi.org/10.1142/s0217979292000438.

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We derive an exact expression for the grand potential of the Hubbard model in d=∞ dimensions. By simplifying the energy transfer between up and down spins we obtain a comprehensive mean-field theory for this model. It is (i) thermodynamically consistent in the entire range of input parameters, (ii) conserving and, (iii) exact in several non-trivial limits, e. g. in the free (U→0), atomic (t→0) and Heisenberg (U≫t, n=1) limit.

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27

LAI, YUN-ZHONG, ZHAN-NING HU, J. Q. LIANG, and FU-CHO PU. "INTEGRABLE XYZ HAMILTONIAN WITH NEXT-NEAREST-NEIGHBOR INTERACTION." International Journal of Modern Physics B 13, no. 07 (March 20, 1999): 847–58. http://dx.doi.org/10.1142/s0217979299000710.

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In this paper, we construct a Hamiltonian of the impurity model with next-nearest-neighbor interaction within the framework of the open boundary Heisenberg XYZ spin chain. This impurity model is an exactly solved one and it degenerates to the integrable XXZ impurity model under the triangular limit. It is the first approach to add the impurities and next-nearest-neighbor interaction to the integrable completely anisotropic Heisenberg spin chain. We find also that the impurity parameters in the bulk are real when the cross parameter is imaginary for the Hermitian Hamiltonian, or vice versa, when the next-nearest-neighbor interaction is introduced. The eigenvalue of the Hamiltonian and the Bethe ansatz equations for the trigonometric limit case are derived also.

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28

Zhuang, Min, Jiahao Huang, and Chaohong Lee. "Entanglement-enhanced test proposal for local Lorentz-symmetry violation via spinor atoms." Quantum 6 (November 14, 2022): 859. http://dx.doi.org/10.22331/q-2022-11-14-859.

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Invariance under Lorentz transformations is fundamental to both the standard model and general relativity. Testing Lorentz-symmetry violation (LSV) via atomic systems attracts extensive interests in both theory and experiment. In several test proposals, the LSV violation effects are described as a local interaction and the corresponding test precision can asymptotically reach the Heisenberg limit via increasing quantum Fisher information (QFI), but the limited resolution of collective observables prevents the detection of large QFI. Here, we propose a multimode many-body quantum interferometry for testing the LSV parameter κ via an ensemble of spinor atoms. By employing an N-atom multimode GHZ state, the test precision can attain the Heisenberg limit Δκ∝1/(F2N) with the spin length F and the atom number N. We find a realistic observable (i.e. practical measurement process) to achieve the ultimate precision and analyze the LSV test via an experimentally accessible three-mode interferometry with Bose condensed spin-1 atoms for example. By selecting suitable input states and unitary recombination operation, the LSV parameter κ can be extracted via realizable population measurement. Especially, the measurement precision of the LSV parameter κ can beat the standard quantum limit and even approach the Heisenberg limit via spin mixing dynamics or driving through quantum phase transitions. Moreover, the scheme is robust against nonadiabatic effect and detection noise. Our test scheme may open up a feasible way for a drastic improvement of the LSV tests with atomic systems and provide an alternative application of multi-particle entangled states.

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29

RAPOSO, E. P., and M. D. COUTINHO-FILHO. "SPIN WAVES AND THE STRONG COUPLING LIMIT IN POLYMERIC HUBBARD CHAINS." Modern Physics Letters B 09, no. 13 (June 10, 1995): 817–22. http://dx.doi.org/10.1142/s0217984995000760.

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We derive the strong-coupling limit of the Hubbard Hamiltonian in a class of polymeric chains displaying a ferrimagnetic structure. The derived Heisenberg Hamiltonian is used to calculate the spin-wave spectrum of the system. It is shown that there is a critical value for an external applied magnetic field above which the ferrimagnetic ordering becomes unstable.

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30

Carfagnini, Marco, and Maria Gordina. "Small deviations and Chung’s law of iterated logarithm for a hypoelliptic Brownian motion on the Heisenberg group." Transactions of the American Mathematical Society, Series B 9, no. 9 (April 19, 2022): 322–42. http://dx.doi.org/10.1090/btran/102.

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31

FLOYD, EDWARD R. "CLASSICAL LIMIT OF THE TRAJECTORY REPRESENTATION OF QUANTUM MECHANICS, LOSS OF INFORMATION AND RESIDUAL INDETERMINACY." International Journal of Modern Physics A 15, no. 09 (April 10, 2000): 1363–78. http://dx.doi.org/10.1142/s0217751x00000604.

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The trajectory representation in the classical limit (ℏ→0) manifests a residual indeterminacy. We show that the trajectory representation in the classical limit goes to neither classical mechanics (Planck's correspondence principle) nor statistical mechanics. This residual indeterminacy is contrasted to Heisenberg uncertainty. We discuss the relationship between residual indeterminacy and 't Hooft's information loss and equivalence classes.

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32

Yin, Chao, and Andrew Lucas. "Heisenberg-limited metrology with perturbing interactions." Quantum 8 (March 28, 2024): 1303. http://dx.doi.org/10.22331/q-2024-03-28-1303.

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We show that it is possible to perform Heisenberg-limited metrology on GHZ-like states, in the presence of generic spatially local, possibly strong interactions during the measurement process. An explicit protocol, which relies on single-qubit measurements and feedback based on polynomial-time classical computation, achieves the Heisenberg limit. In one dimension, matrix product state methods can be used to perform this classical calculation, while in higher dimensions the cluster expansion underlies the efficient calculations. The latter approach is based on an efficient classical sampling algorithm for short-time quantum dynamics, which may be of independent interest.

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33

Viktor, Gerasimenko. "Heisenberg picture of quantum kinetic evolution in mean-field limit." Kinetic & Related Models 4, no. 1 (2011): 385–99. http://dx.doi.org/10.3934/krm.2011.4.385.

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34

Dunningham, J., and T. Kim. "Using quantum interferometers to make measurements at the Heisenberg limit." Journal of Modern Optics 53, no. 4 (March 10, 2006): 557–71. http://dx.doi.org/10.1080/09500340500443268.

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35

Napolitano, M., M. Koschorreck, B. Dubost, N. Behbood, R. J. Sewell, and M. W. Mitchell. "Interaction-based quantum metrology showing scaling beyond the Heisenberg limit." Nature 471, no. 7339 (March 2011): 486–89. http://dx.doi.org/10.1038/nature09778.

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36

Holland, M. J., and K. Burnett. "Interferometric detection of optical phase shifts at the Heisenberg limit." Physical Review Letters 71, no. 9 (August 30, 1993): 1355–58. http://dx.doi.org/10.1103/physrevlett.71.1355.

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37

Nosraty, Farzam. "Heisenberg Limit Phase Sensitivity in the Presence of Decoherence Channels." Communications in Theoretical Physics 65, no. 2 (February 1, 2016): 225–30. http://dx.doi.org/10.1088/0253-6102/65/2/225.

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38

Tsarev, D. V., and S. M. Arakelian. "Quantum metrology beyond Heisenberg limit with entangled matter wave solitons." Optics Express 26, no. 15 (July 19, 2018): 19583. http://dx.doi.org/10.1364/oe.26.019583.

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39

Yi, Hong-Gang, and Rong-Hua Chen. "Quantum Fisher Information and Heisenberg Limit in Multi-qubit State." International Journal of Theoretical Physics 52, no. 1 (September 9, 2012): 233–38. http://dx.doi.org/10.1007/s10773-012-1324-2.

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40

Tartaglia, Angelo, and Matteo Luca Ruggiero. "From Kerr to Heisenberg." Entropy 23, no. 3 (March 7, 2021): 315. http://dx.doi.org/10.3390/e23030315.

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In this paper, we consider the space-time of a charged mass endowed with an angular momentum. The geometry is described by the exact Kerr–Newman solution of the Einstein equations. The peculiar symmetry, though exact, is usually described in terms of the gravito-magnetic field originated by the angular momentum of the source. A typical product of this geometry is represented by the generalized Sagnac effect. We write down the explicit form for the right/left asymmetry of the times of flight of two counter-rotating light beams along a circular trajectory. Letting the circle shrink to the origin the asymmetry stays finite. Furthermore it becomes independent both from the charge of the source (then its electromagnetic field) and from Newton’s constant: it is then associated only to the symmetry produced by the gravitomagnetic field. When introducing, for the source, the spin of a Fermion, the lowest limit of the Heisenberg uncertainty formula for energy and time appears.

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41

BATLE, J., A. PLASTINO, A. R. PLASTINO, and M. CASAS. "DISCORD-ENTANGLEMENT INTERPLAY IN THE THERMODYNAMIC LIMIT: THE XY-MODEL." International Journal of Quantum Information 11, no. 01 (February 2013): 1350003. http://dx.doi.org/10.1142/s0219749913500032.

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We investigate thermal properties of quantum correlations in the thermodynamic limit with reference to the XY-model and the finite two-qubit Heisenberg model. Although this model has been the subject of active entanglement-research, the bulk of the pertinent work refers to finite instantiations. As a consequence, the temperature cannot be properly defined in such circumstances, a problem that is overcome here. Our effort should be of interest because quantum discord notion.

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42

Ge, Zhong. "Collapsing Riemannian Metrics to Carnot-Caratheodory Metrics and Laplacians to Sub-Laplacians." Canadian Journal of Mathematics 45, no. 3 (June 1, 1993): 537–53. http://dx.doi.org/10.4153/cjm-1993-028-6.

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AbstractWe study the asymptotic behavior of the Laplacian on functions when the underlying Riemannian metric is collapsed to a Carnot-Carathéodory metric. We obtain a uniform short time asymptotics for the trace of the heat kernel in the case when the limit Carnot-Carathéodory metric is almost Heisenberg, the limit of which is the result of Beal-Greiner-Stanton, and Stanton-Tartakoff.

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43

Zhang, Pan-Pan, Zhong-Yang Gao, Yu-Liang Xu, Chun-Yang Wang, and Xiang-Mu Kong. "Phase diagrams, quantum correlations and critical phenomena of antiferromagnetic Heisenberg model on diamond-type hierarchical lattices." Quantum Science and Technology 7, no. 2 (March 22, 2022): 025024. http://dx.doi.org/10.1088/2058-9565/ac57f4.

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Abstract The spin-1/2 antiferromagnetic (AF) Heisenberg systems are studied on three typical diamond-type hierarchical lattices (systems A, B and C) with fractal dimensions 1.63, 2 and 2.58, respectively, and the phase diagrams, critical phenomena and quantum correlations are calculated by a combination of the equivalent transformation and real-space renormalization group methods. We find that there exist a reentrant behavior for system A and a finite temperature phase transition in the isotropic Heisenberg limit for system C (not for system B). Unlike the ferromagnetic case, the Néel temperatures of AF systems A and B are inversely proportional to ln Δ c − Δ (when Δ → Δc) and ln Δ (when Δ → 0), respectively. And we also find that there is a turning point of quantum correlation in the isotropic Heisenberg limit Δ = 0 where there is a ‘peak’ of the contour and no matter how large the size of system is, quantum correlation will change to zero in the Ising limit for the three systems. The quantum correlation decreases with the increase of lattice size L and it is almost zero when L ⩾ 30 for system A, and for systems B and C, they still exist when L is larger than that of system A. Moreover, we discuss the effects of quantum fluctuation and analyze the errors of results in the above three systems, which are induced by the noncommutativity.

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MAGNEA, LORENZO, RODOLFO RUSSO, and STEFANO SCIUTO. "TWO-LOOP EULER–HEISENBERG EFFECTIVE ACTIONS FROM CHARGED OPEN STRINGS." International Journal of Modern Physics A 21, no. 03 (January 30, 2006): 533–57. http://dx.doi.org/10.1142/s0217751x06025110.

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We present the multiloop partition function of open bosonic string theory in the presence of a constant gauge field strength, and discuss its low-energy limit. The result is written in terms of twisted determinants and differentials on higher-genus Riemann surfaces, for which we provide an explicit representation in the Schottky parametrization. In the field theory limit, we recover from the string formula the two-loop Euler–Heisenberg effective action for adjoint scalars minimally coupled to the background gauge field.

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Tessarotto, Massimo, and Claudio Cremaschini. "The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity." Entropy 22, no. 11 (October 26, 2020): 1209. http://dx.doi.org/10.3390/e22111209.

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The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy Principle in the framework of Quantum Gravity. The starting point is the establishment of the so-called time-conjugate momentum inequalities holding for non-relativistic and relativistic Quantum Mechanics. The validity of analogous Heisenberg inequalities in quantum gravity, which must be based on strictly physically observable quantities (i.e., necessarily either 4-scalar or 4-vector in nature), is shown to require the adoption of a manifestly covariant and unitary quantum theory of the gravitational field. Based on the prescription of a suitable notion of Hilbert space scalar product, the relevant Heisenberg inequalities are established. Besides the coordinate-conjugate momentum inequalities, these include a novel proper-time-conjugate extended momentum inequality. Physical implications and the connection with the deterministic limit recovering General Relativity are investigated.

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HU, MING-LIANG. "IMPURITY ENTANGLEMENT IN THE OPEN-ENDED HEISENBERG CHAINS." Modern Physics Letters B 22, no. 29 (November 20, 2008): 2849–55. http://dx.doi.org/10.1142/s0217984908017357.

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By using the concept of concurrence, we study pairwise entanglement between the two end spins in the open-ended Heisenberg XXX and XY chains up to ten spins. The results show that by introducing two boundary impurities, one can obtain maximum entanglement at the limit of the impurity parameter |J1| ≪ J for the even-number qubits. When |J1/J| > 0, the entanglement always decreases with the increase in the absolute value of J1/J, and for the Heisenberg XXX chain, C disappears when J1/J exceeds a certain critical point Jic, and attains an asymptotic value C0 when |J1| ≫ J(J1 < 0), while for the Heisenberg XY chain, C always disappears when |J1/J| exceeds a certain critical point Jic. Both C0 and Jic decrease with the increase of the length of the chain.

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Farooq, Ahmad, Uman Khalid, Junaid ur Rehman, and Hyundong Shin. "Robust Quantum State Tomography Method for Quantum Sensing." Sensors 22, no. 7 (March 30, 2022): 2669. http://dx.doi.org/10.3390/s22072669.

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Reliable and efficient reconstruction of pure quantum states under the processing of noisy measurement data is a vital tool in fundamental and applied quantum information sciences owing to communication, sensing, and computing. Specifically, the purity of such reconstructed quantum systems is crucial in surpassing the classical shot-noise limit and achieving the Heisenberg limit, regarding the achievable precision in quantum sensing. However, the noisy reconstruction of such resourceful sensing probes limits the quantum advantage in precise quantum sensing. For this, we formulate a pure quantum state reconstruction method through eigenvalue decomposition. We show that the proposed method is robust against the depolarizing noise; it remains unaffected under high strength white noise and achieves quantum state reconstruction accuracy similar to the noiseless case.

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BENOIT, J., R. DANDOLOFF, and A. SAXENA. "HEISENBERG SPINS ON A CYLINDER SECTION." International Journal of Modern Physics B 14, no. 19n20 (August 10, 2000): 2093–100. http://dx.doi.org/10.1142/s0217979200001242.

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Classical Heisenberg spins in the continuum limit (i.e. the nonlinear σ-model) are studied on an elastic cylinder section with homogeneous boundary conditions. The latter may serve as a physical realization of magnetically coated microtubules and cylindrical membranes. The corresponding rigid cylinder model exhibits topological soliton configurations with geometrical frustration due to the finite length of the cylinder section. Assuming small and smooth deformations allows to find shapes of the elastic support by relaxing the rigidity constraint: an inhomogeneous Lamé equation arises. Finally, this leads to a novel geometric effect: a global shrinking of the cylinder section with swellings.

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Bilski, Jakub, Suddhasattwa Brahma, Antonino Marcianò, and Jakub Mielczarek. "Klein–Gordon field from the XXZ Heisenberg model." International Journal of Modern Physics D 28, no. 01 (January 2019): 1950020. http://dx.doi.org/10.1142/s0218271819500202.

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We examine the recently introduced idea of Spin-Field Correspondence (SFC) focusing on the example of the spin system described by the XXZ Heisenberg model with external magnetic field. The Hamiltonian of the resulting nonlinear scalar field theory is derived for arbitrary value of the anisotropy parameter [Formula: see text]. We show that the linear scalar field theory is reconstructed in the large spin limit. For [Formula: see text], a nonrelativistic scalar field theory satisfying the Born reciprocity principle is recovered. As expected, for the vanishing anisotropy parameter [Formula: see text], the standard relativistic Klein–Gordon field is obtained. Various aspects of the obtained class of the scalar fields are studied, including the fate of the relativistic symmetries and the properties of the emerging interaction terms. We show that, in a certain limit, the so-called polymer quantization of the field variables is recovered. This and other discussed properties suggest a possible relevance of the considered framework in the context of quantum gravity.

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Hou, Zhibo, Jun-Feng Tang, Hongzhen Chen, Haidong Yuan, Gou-Yong Xiang, Chuan-Feng Li, and Guang-Can Guo. "Zero–trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations." Science Advances 7, no. 1 (January 2021): eabd2986. http://dx.doi.org/10.1126/sciadv.abd2986.

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Quantum estimation of a single parameter has been studied extensively. Practical applications, however, typically involve multiple parameters, for which the ultimate precision is much less understood. Here, by relating the precision limit directly to the Heisenberg uncertainty relation, we show that to achieve the highest precisions for multiple parameters at the same time requires the saturation of multiple Heisenberg uncertainty relations simultaneously. Guided by this insight, we experimentally demonstrate an optimally controlled multipass scheme, which saturates three Heisenberg uncertainty relations simultaneously and achieves the highest precisions for the estimation of all three parameters in SU(2) operators. With eight controls, we achieve a 13.27-dB improvement in terms of the variance (6.63 dB for the SD) over the classical scheme with the same loss. As an experiment demonstrating the simultaneous achievement of the ultimate precisions for multiple parameters, our work marks an important step in multiparameter quantum metrology with wide implications.

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