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Peter Talkner - One of the best experts on this subject based on the ideXlab platform.
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Quantum Fluctuation theorems and power measurements
New Journal of Physics, 2015Co-Authors: Prasanna B Venkatesh, Gentaro Watanabe, Peter TalknerAbstract:Work in the paradigm of the Quantum Fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system's dynamics is frozen in the power measurement basis due to the Quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics.
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generalized energy measurements and modified transient Quantum Fluctuation theorems
Physical Review E, 2014Co-Authors: Gentaro Watanabe, Prasanna B Venkatesh, Peter TalknerAbstract:Determining the work which is supplied to a system by an external agent provides a crucial step in any experimental realization of transient Fluctuation relations. This, however, poses a problem for Quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient Fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modified Crooks relation and Jarzynski equality are found for Gaussian energy measurements. These can be obtained by a sequence of sufficiently many generalized measurements which need not be Gaussian. In accordance with the central limit theorem, this leads to an effective error reduction in the individual measurements and even yields a projective measurement in the limit of infinite repetitions.
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Quantum Fluctuation theorems and generalized measurements during the force protocol
Physical Review E, 2014Co-Authors: Gentaro Watanabe, Prasanna B Venkatesh, Peter Talkner, Michele Campisi, Peter HanggiAbstract:Generalized measurements of an observable performed on a Quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with previous studies by M. Campisi, P. Talkner, and P. Hanggi [Phys. Rev. Lett. 105, 140601 (2010); Phys. Rev. E 83, 041114 (2011)], we find that these Fluctuation relations are satisfied for projective measurements; however, for generalized measurements special conditions on the operators determining the measurements need to be met. For the Jarzynski equality to hold, the measurement operators of the forward protocol must be normalized in a particular way. The Crooks relation additionally entails that the backward and forward measurement operators depend on each other. Yet, quite some freedom is left as to how the two sets of operators are interrelated. This ambiguity is removed if one considers selective measurements, which are specified by a joint probability density function of work and measurement results of the considered observable. We find that the respective forward and backward joint probabilities satisfy the Crooks relation only if the measurement operators of the forward and backward protocols are the time-reversed adjoints of each other. In this case, the work probability density function conditioned on the measurement result satisfies a modified Crooks relation. The modification appears as a protocol-dependent factor that can be expressed by the information gained by the measurements during the forward and backward protocols. Finally, detailed Fluctuation theorems with an arbitrary number of intervening measurements are obtained.
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colloquium Quantum Fluctuation relations foundations and applications
Reviews of Modern Physics, 2011Co-Authors: Michele Campisi, Peter Hanggi, Peter TalknerAbstract:Two fundamental ingredients play a decisive role in the foundation of Fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two pillars the reader is guided through a self-contained exposition of the theory and applications of Quantum Fluctuation relations. These are exact results that constitute the fulcrum of the recent development of nonequilibrium thermodynamics beyond the linear response regime. The material is organized in a way that emphasizes the historical connection between Quantum Fluctuation relations and (non)linear response theory. A number of fundamental issues are clarified which were not completely settled in the prior literature. The main focus is on (i) work Fluctuation relations for transiently driven closed or open Quantum systems, and (ii) on Fluctuation relations for heat and matter exchange in Quantum transport settings. Recently performed and proposed experimental applications are presented and discussed.
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microcanonical Quantum Fluctuation theorems
Physical Review E, 2008Co-Authors: Peter Talkner, Peter Hanggi, M MorilloAbstract:Previously derived expressions for the characteristic function of work performed on a Quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate spectra. In the particular case of microcanonical initial states, explicit expressions for the characteristic function and the corresponding probability density of work are formulated. Their classical limit as well as their relations to the corresponding canonical expressions are discussed. A Fluctuation theorem is derived that expresses the ratio of probabilities of work for a process and its time reversal to the ratio of densities of states of the microcanonical equilibrium systems with corresponding initial and final Hamiltonians. From this Crooks-type Fluctuation theorem a relation between entropies of different systems can be derived which does not involve the time-reversed process. This entropy-from-work theorem provides an experimentally accessible way to measure entropies.
Peter Hanggi - One of the best experts on this subject based on the ideXlab platform.
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Quantum Fluctuation theorems and generalized measurements during the force protocol
Physical Review E, 2014Co-Authors: Gentaro Watanabe, Prasanna B Venkatesh, Peter Talkner, Michele Campisi, Peter HanggiAbstract:Generalized measurements of an observable performed on a Quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with previous studies by M. Campisi, P. Talkner, and P. Hanggi [Phys. Rev. Lett. 105, 140601 (2010); Phys. Rev. E 83, 041114 (2011)], we find that these Fluctuation relations are satisfied for projective measurements; however, for generalized measurements special conditions on the operators determining the measurements need to be met. For the Jarzynski equality to hold, the measurement operators of the forward protocol must be normalized in a particular way. The Crooks relation additionally entails that the backward and forward measurement operators depend on each other. Yet, quite some freedom is left as to how the two sets of operators are interrelated. This ambiguity is removed if one considers selective measurements, which are specified by a joint probability density function of work and measurement results of the considered observable. We find that the respective forward and backward joint probabilities satisfy the Crooks relation only if the measurement operators of the forward and backward protocols are the time-reversed adjoints of each other. In this case, the work probability density function conditioned on the measurement result satisfies a modified Crooks relation. The modification appears as a protocol-dependent factor that can be expressed by the information gained by the measurements during the forward and backward protocols. Finally, detailed Fluctuation theorems with an arbitrary number of intervening measurements are obtained.
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colloquium Quantum Fluctuation relations foundations and applications
Reviews of Modern Physics, 2011Co-Authors: Michele Campisi, Peter Hanggi, Peter TalknerAbstract:Two fundamental ingredients play a decisive role in the foundation of Fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two pillars the reader is guided through a self-contained exposition of the theory and applications of Quantum Fluctuation relations. These are exact results that constitute the fulcrum of the recent development of nonequilibrium thermodynamics beyond the linear response regime. The material is organized in a way that emphasizes the historical connection between Quantum Fluctuation relations and (non)linear response theory. A number of fundamental issues are clarified which were not completely settled in the prior literature. The main focus is on (i) work Fluctuation relations for transiently driven closed or open Quantum systems, and (ii) on Fluctuation relations for heat and matter exchange in Quantum transport settings. Recently performed and proposed experimental applications are presented and discussed.
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microcanonical Quantum Fluctuation theorems
Physical Review E, 2008Co-Authors: Peter Talkner, Peter Hanggi, M MorilloAbstract:Previously derived expressions for the characteristic function of work performed on a Quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate spectra. In the particular case of microcanonical initial states, explicit expressions for the characteristic function and the corresponding probability density of work are formulated. Their classical limit as well as their relations to the corresponding canonical expressions are discussed. A Fluctuation theorem is derived that expresses the ratio of probabilities of work for a process and its time reversal to the ratio of densities of states of the microcanonical equilibrium systems with corresponding initial and final Hamiltonians. From this Crooks-type Fluctuation theorem a relation between entropies of different systems can be derived which does not involve the time-reversed process. This entropy-from-work theorem provides an experimentally accessible way to measure entropies.
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the tasaki crooks Quantum Fluctuation theorem
Journal of Physics A, 2007Co-Authors: Peter Talkner, Peter HanggiAbstract:Starting out from the recently established Quantum correlation function expression of the characteristic function for the work performed by a force protocol on the system in Talkner et al (2007 Phys. Rev. E 75 050102 (Preprint cond-mat/0703213)) the Quantum version of the Crooks Fluctuation theorem is shown to emerge almost immediately by the mere application of an inverse Fourier transformation.
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the tasaki crooks Quantum Fluctuation theorem
arXiv: Statistical Mechanics, 2007Co-Authors: Peter Talkner, Peter HanggiAbstract:Starting out from the recently established Quantum correlation function expression of the characteristic function for the work performed by a force protocol on the system [cond-mat/0703213] the Quantum version of the Crooks Fluctuation theorem is shown to emerge almost immediately by the mere application of an inverse Fourier transformation.
Fei Zhou - One of the best experts on this subject based on the ideXlab platform.
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Quantum-Fluctuation-driven coherent spin dynamics in small condensates
Physical Review A, 2008Co-Authors: Xiaoling Cui, Yupeng Wang, Fei ZhouAbstract:We have studied the Quantum spin dynamics of small condensates of cold sodium atoms. For a condensate initially prepared in a mean-field ground state, we show that coherent spin dynamics is purely driven by Quantum Fluctuations of collective spin coordinates and can be tuned by quadratic Zeeman coupling and magnetization. This dynamics in small condensates can be probed in a high-finesse optical cavity where the temporal behaviors of the excitation spectra of a coupled condensate-photon system reveal the time evolution of populations of atoms at different hyperfine spin states.
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Tunable Quantum Fluctuation-Controlled Coherent Spin Dynamics
Physical Review A, 2008Co-Authors: Jun Liang Song, Fei ZhouAbstract:Temporal evolution of a macroscopic condensate of ultracold atoms is usually driven by mean-field potentials, either due to scattering between atoms or due to coupling to external fields; and coherent Quantum dynamics of this type have been observed in various cold atom experiments. In this paper, we report results of studies of a class of Quantum spin dynamics which are purely driven by zero point Quantum Fluctuations of spin collective coordinates. Unlike the usual mean-field coherent dynamics, Quantum-Fluctuation-controlled spin dynamics (or QFCSD) studied here are very sensitive to variation of Quantum Fluctuations and the corresponding driving potentials induced by zero point motions can be tuned by four to five orders of magnitude using optical lattices. These dynamics have unique dependence on optical lattice potential depths and quadratic Zeeman fields. We also find that thermal Fluctuations generally can further enhance the induced potentials although the enhancement in deep optical lattices is much less substantial than in traps or shallow lattices. QFCSD can be potentially used to calibrate Quantum Fluctuations and investigate correlated Fluctuations and various universal scaling properties near Quantum critical points.
Gentaro Watanabe - One of the best experts on this subject based on the ideXlab platform.
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Quantum Fluctuation theorems and power measurements
New Journal of Physics, 2015Co-Authors: Prasanna B Venkatesh, Gentaro Watanabe, Peter TalknerAbstract:Work in the paradigm of the Quantum Fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system's dynamics is frozen in the power measurement basis due to the Quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics.
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generalized energy measurements and modified transient Quantum Fluctuation theorems
Physical Review E, 2014Co-Authors: Gentaro Watanabe, Prasanna B Venkatesh, Peter TalknerAbstract:Determining the work which is supplied to a system by an external agent provides a crucial step in any experimental realization of transient Fluctuation relations. This, however, poses a problem for Quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient Fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modified Crooks relation and Jarzynski equality are found for Gaussian energy measurements. These can be obtained by a sequence of sufficiently many generalized measurements which need not be Gaussian. In accordance with the central limit theorem, this leads to an effective error reduction in the individual measurements and even yields a projective measurement in the limit of infinite repetitions.
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Quantum Fluctuation theorems and generalized measurements during the force protocol
Physical Review E, 2014Co-Authors: Gentaro Watanabe, Prasanna B Venkatesh, Peter Talkner, Michele Campisi, Peter HanggiAbstract:Generalized measurements of an observable performed on a Quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with previous studies by M. Campisi, P. Talkner, and P. Hanggi [Phys. Rev. Lett. 105, 140601 (2010); Phys. Rev. E 83, 041114 (2011)], we find that these Fluctuation relations are satisfied for projective measurements; however, for generalized measurements special conditions on the operators determining the measurements need to be met. For the Jarzynski equality to hold, the measurement operators of the forward protocol must be normalized in a particular way. The Crooks relation additionally entails that the backward and forward measurement operators depend on each other. Yet, quite some freedom is left as to how the two sets of operators are interrelated. This ambiguity is removed if one considers selective measurements, which are specified by a joint probability density function of work and measurement results of the considered observable. We find that the respective forward and backward joint probabilities satisfy the Crooks relation only if the measurement operators of the forward and backward protocols are the time-reversed adjoints of each other. In this case, the work probability density function conditioned on the measurement result satisfies a modified Crooks relation. The modification appears as a protocol-dependent factor that can be expressed by the information gained by the measurements during the forward and backward protocols. Finally, detailed Fluctuation theorems with an arbitrary number of intervening measurements are obtained.
M Takigawa - One of the best experts on this subject based on the ideXlab platform.
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field enhanced Quantum Fluctuation in an s 1 2 frustrated square lattice
Physical Review B, 2018Co-Authors: Hironori Yamaguchi, Y Sasaki, Tsuyoshi Okubo, Makoto Yoshida, Takanori Kida, Masayuki Hagiwara, Yohei Kono, Shunichiro Kittaka, Toshiro Sakakibara, M TakigawaAbstract:We present a new model compound with the S = 1/2 frustrated square lattice composed of the charge-transfer salt (o-MePy-V)PF6. Ab initio calculations indicate the formation of an S = 1/2 square lattice, in which six types of nearest-neighbor ferromagnetic- and antiferromagnetic interactions cause frustration. By applying a magnetic field, we observe an unusually gradual increase of magnetization and a subsequent 1/2-plateau-like behavior. A numerical analysis using the tensor network method qualitatively demonstrates such behaviors and suggests a collinear ordered state and a field-enhanced Quantum Fluctuation. Furthermore, the local magnetization and T1^-1 probed by nuclear magnetic resonance measurements support these findings.
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field enhanced Quantum Fluctuation in an s 1 2 frustrated square lattice
Physical Review B, 2018Co-Authors: Hironori Yamaguchi, Y Sasaki, Takanori Kida, Masayuki Hagiwara, Yohei Kono, Shunichiro Kittaka, Toshiro Sakakibara, Tatsuya Okubo, Masahiro Yoshida, M TakigawaAbstract:We present a new model compound with the $S=1/2$ frustrated square lattice composed of the charge-transfer salt ($o$-MePy-V)${\mathrm{PF}}_{6}$. $Ab\phantom{\rule{4pt}{0ex}}initio$ calculations indicate the formation of an $S=1/2$ square lattice, in which six types of nearest-neighbor ferromagnetic and antiferromagnetic interactions cause frustration. By applying a magnetic field, we observe an unusually gradual increase of magnetization and a subsequent 1/2-plateau-like behavior. A numerical analysis using the tensor network method qualitatively demonstrates such behaviors and suggests a collinear ordered state and a field-enhanced Quantum Fluctuation. Furthermore, the local magnetization and ${T}_{1}^{\ensuremath{-}1}$ probed by nuclear magnetic resonance measurements support these findings.
