Anomalously Slow Cross Symmetry Phase Relaxation, Thermalized Non-Equilibrated Matter and Quantum Computing Beyond the Quantum Chaos Border

J. Flores; M. Bienert; S.Yu. Kun; T.H. Seligman

REVIEW

Anomalously Slow Cross Symmetry Phase Relaxation, Thermalized Non-Equilibrated Matter and Quantum Computing Beyond the Quantum Chaos Border

M. Bienert, J. Flores, S.Yu. Kun, T.H. Seligman

Quantum Physics · Submitted 27 Feb 2006 · 34 references

Pith's verdict: Interesting speculation, but the quantitative claim is undermined by a correlation amplitude that exceeds unity and by unexcluded non-compound photoproton emission; not ready for publication as is.

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CitationJ. Flores, M. Bienert, S.Yu. Kun, T.H. Seligman. "Anomalously Slow Cross Symmetry Phase Relaxation, Thermalized Non-Equilibrated Matter and Quantum Computing Beyond the Quantum Chaos Border." arXiv:quant-ph/0602224 (2006). https://pith.science/paper/UBPME4GC

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Editor's note

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The new thing here is the application of the authors' earlier phase-relaxation idea to a photonuclear reaction, Bi(γ,p), with a claimed eight-orders-of-magnitude separation between phase and energy relaxation. The paper is short, readable, and honest about its own limits: they explicitly state that the theoretical evaluation of β is an open problem. If the central claim were right, it would be an important result for statistical reactions and for the quantum-computing-beyond-quantum-chaos idea. That's the upside.

The downsides are substantial and, in one place, fatal to the quantitative extraction. First, the correlation formula in Eq. (3) gives (1 + β/Γ_cn) as the ratio of the off-diagonal S-matrix correlation to the geometric mean of the diagonal intensities. For any positive β this exceeds 1, and at the fitted value β/Γ_cn = 0.11 it is 1.11. That violates the Schwarz inequality for a normalized correlation. This is not a minor point; it makes the fitted β unphysical as a correlation coefficient. The authors never address this.

Second, the analysis assumes the entire angular distribution is evaporative compound-nucleus decay. The exponential low-energy spectrum in Fig. 1 shows thermalization, but it does not show that the forward peaking in Fig. 2 is evaporative. Direct, semi-direct, or pre-equilibrium photoproton emission can also produce forward-peaked angular distributions via E1–E2 interference without any cross-spin-parity phase memory. The paper does not exclude these mechanisms. With a single old 1953 dataset, no error bars, and a four-parameter fit, the extracted β is not identifiable as a phase relaxation width.

Third, even granting the model, β is fitted, not predicted. The authors admit its theoretical evaluation is open, so the eight-orders claim is a product of the fit, not an independent falsifiable prediction. That would be acceptable as a hypothesis, but it is presented here as a demonstration.

That said, the paper is not nonsense. The empirical asymmetry is real and the exponential spectrum is real. The question is whether the asymmetry carries the interpretation they put on it. The flaws are addressable: redo the fit with uncertainties, fix the correlation bound, and model non-compound contributions. If the asymmetry survives those tests, the claim would deserve serious attention.

My recommendation: send it to peer review, but expect heavy revision. The referee should push on the correlation amplitude immediately and require an explicit treatment of non-compound emission. As it stands, I would not cite it; the central number does not hold up.

Referee report

Significance

If the extraction were sound, the result would be striking: it would imply that a highly excited many-body system can retain directional memory for times far longer than energy thermalization, with consequences for the understanding of quantum relaxation and for proposals to operate quantum computers in the regime of strongly overlapping resonances. The paper is commendably explicit about the data source, the four fitting parameters, and the fact that the theoretical evaluation of β is currently an open problem. However, the central quantitative claim rests on a single old dataset, a fit without reported uncertainties, and a correlation formula whose numerical output violates a basic inequality; these problems prevent the claim from being accepted as demonstrated.

Major objections (4)

[Section 3, Eq. (3)] As printed, the correlation amplitude in Eq. (3) is (1 + β/Γ_cn), which exceeds unity for any positive β; at the fitted value β/Γ_cn = 0.11 it equals 1.11. A correlation coefficient between two S-matrix elements cannot exceed 1 in modulus, so the formula violates the Schwarz inequality. Since Eq. (3) is the central object that converts the angular asymmetry into a phase relaxation width, the quantitative extraction of β is not admissible unless the definition of β or the normalization in Eq. (3) is corrected.
[Section 3, Eqs. (2)–(5)] The fit assigns the entire measured angular distribution for ε = 2–8 MeV to compound-nucleus evaporation. The exponential shape of the angle-integrated scaled spectrum in Fig. 1 does not exclude forward-peaked direct, semi-direct, or pre-equilibrium photoproton emission, which are standard contributions in photonuclear reactions at 24 MeV and can produce forward peaking through E1–E2 interference without any cross-spin-parity correlation of compound S-matrix elements. The manuscript neither cites nor subtracts such contributions. If a substantial part of the forward peaking is non-compound, β/Γ_cn = 0.11 is not a measure of phase relaxation and the eight-orders-of-magnitude separation is unsupported.
[Section 3, Fig. 2 fit] The paper reports four fitted parameters (A, B, C, β/Γ_cn) with no error bars on the experimental points, no parameter uncertainties, and no goodness-of-fit statistic. The central result β ≈ 0.01 eV also combines Γ_cn ≈ 0.1 eV from systematics and Γ_spr ≈ 2–4.5 MeV from [23,15], both order-of-magnitude estimates, without any propagated uncertainty. Without such information the claimed eight-order-of-magnitude separation cannot be assessed, especially since the fitted β/Γ_cn = 0.11 appears to come from a single dataset with unknown systematic errors.
[Section 3, final paragraph] The manuscript states that the theoretical evaluation of β is 'currently an open problem.' Since no independent calculation or independent experimental constraint on β is provided, β functions only as a fit parameter within the authors' framework. The identification of the fitted β with a physical phase relaxation width is therefore a postulate rather than a demonstrated property; the reader is offered no benchmark that would validate the framework or the order-of-magnitude result.

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The paper

The paper claims

A thermalized quantum many-body system can retain phase memory of how it was formed for a time about eight orders of magnitude longer than thermalization itself.

The reading

This paper claims that a highly excited quantum many-body system can reach full energy thermalization while still preserving a directional memory of how it was formed. The evidence is the Bi($\gamma$,p) reaction: the evaporated proton spectrum has an exponential slope of 0.55 MeV, as expected from a thermalized compound nucleus, yet the proton angular distribution is strongly asymmetric about 90 degrees. Fitting the standard gamma-reaction cross-section formula with a single cross-symmetry correlation parameter gives $\beta/\Gamma_{\mathrm{cn}}=0.11$, and with $\Gamma_{\mathrm{cn}}\simeq 0.1$ eV this yields a phase relaxation time about eight orders of magnitude longer than the thermalization time $\hbar/\Gamma_{\mathrm{spr}}$. If true, this means thermalized but non-equilibrated matter can survive for $\sim 6\times10^{-14}$ s, and it re-opens the question of whether quantum computation with $n\simeq 100$\textendash 1000 qubits could run far beyond the quantum chaos border.

What carries the argument

The central object is the cross-symmetry phase relaxation width $\beta$ introduced in Eq. (3): a parameter controlling the correlation between fluctuating S-matrix elements with different total spin and parity, $\langle S_{L_1}^* S_{L_2}\rangle = [\langle|S_{L_1}|^2\rangle\langle|S_{L_2}|^2\rangle]^{1/2}(1+\beta/\Gamma_{\mathrm{cn}})$. It is the inverse time over which the interference between states of different symmetry survives the energy averaging, i.e. the lifetime of the memory of the beam direction. Analysis of the Bi($\gamma$,p) angular distribution with this formula fixes $\beta/\Gamma_{\mathrm{cn}}=0.11$, and estimating $\Gamma_{\mathrm{cn}}\simeq 0.1$ eV from width systematics gives $\beta\simeq 0.01$ eV against $\Gamma_{\mathrm{spr}}\simeq 2$\textendash 4.5 MeV. This ratio is what carries the entire argument: without the tiny $\beta$, the angular asymmetry would vanish and the evaporating protons would be symmetric about 90 degrees.

Extended reading notes

Core claim

On the paper's own terms, the discovery is that complete energy thermalization in a compound nucleus does not imply the erasure of all phase information: the angular distribution of evaporating protons retains a forward-backward asymmetry that can only come from spin-parity off-diagonal correlations between S-matrix elements surviving energy averaging. The paper identifies the inverse lifetime of these correlations, the cross-symmetry phase relaxation width $\beta$, as the quantity that is anomalously small: $\beta \simeq 0.01$ eV against an estimated spreading width $\Gamma_{\mathrm{spr}} \simeq 2$\textendash 4.5 MeV. The resulting phase memory time $\tau_{\mathrm{ph}} = \hbar/\beta$ is about eight orders of magnitude longer than the thermalization time, so the compound nucleus behaves as a thermalized yet non-equilibrated many-body state. The same effect was previously seen in nucleon-induced reactions with a five-order separation; the electromagnetic entrance channel studied here is presented as a step closer to loading mechanisms in proposed quantum computers.

Load-bearing premise

The argument assumes that the entire measured forward-peaked angular distribution is compound-nucleus evaporation captured by the standard formula with one cross-symmetry parameter $\beta$; if direct, semi-direct, or pre-equilibrium photoproton emission contributes substantially to the forward peaking, the fitted $\beta$ would not measure phase relaxation and the eight-order separation collapses.

Editorial extensions

If this is right

Energy thermalization and phase relaxation are separate clocks in highly excited many-body systems, and the phase clock can be slower by many orders of magnitude.
A compound nucleus can serve as a physical demonstration that useful information about the loading channel survives for $\sim 6\times10^{-14}$ s, long after the $\sim 3\times10^{-22}$ s onset of quantum chaos.
The analysis suggests that quantum computing protocols could in principle run on timescales set by $\hbar/\beta$, not $\hbar/\Gamma_{\mathrm{spr}}$, extending feasible qubit numbers toward $n\simeq 100$\textendash 1000.
Because the entrance channel here is electromagnetic, the result is closer to the loading mechanisms envisioned for proposed quantum computers than the earlier nucleon-induced reactions.
The effect is not limited to this reaction: the same formalism predicts non-vanishing spin-parity off-diagonal correlations in other strongly overlapping resonance reactions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Extending beyond the paper, a decisive microscopic derivation of $\beta$ \textendash{} currently stated to be an open problem \textendash{} would need to explain why interference between different spin-parity components survives energy averaging in a Hilbert space of effective dimension $\sim 10^{16}$.
If the interpretation is right, the same $\beta$ should also appear in other electromagnetic entrance channels, such as $(\gamma,n)$ or electron-induced reactions, whose angular distributions could be checked against existing data.
A testable extension would look for analogous long-lived directional memory in cold-atom or mesoscopic systems with strong interactions and large effective Hilbert spaces, transferring the nuclear finding to a controlled setting.
The quantum-computing claim is illustrative rather than a device proposal: the load-bearing insight is that coherence lifetimes in dense interacting many-body systems are not bounded by the local thermalization time.

Original abstract

Thermalization in highly excited quantum many-body system does not necessarily mean a complete memory loss of the way the system was formed. This effect may pave a way for a quantum computing, with a large number of qubits $n\simeq 100$--1000, far beyond the quantum chaos border. One of the manifestations of such a thermalized non-equilibrated matter is revealed by a strong asymmetry around 90$^\circ $ c.m. of evaporating proton yield in the Bi($\gamma$,p) photonuclear reaction. The effect is described in terms of anomalously slow cross symmetry phase relaxation in highly excited quantum many-body systems with exponentially large Hilbert space dimensions. In the above reaction this phase relaxation is about eight orders of magnitude slower than energy relaxation (thermalization).

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,358 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.29 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Thermalization in highly excited quantum many-body system does not necessarily mean a complete memory loss of the way the system was formed. This effect may pave a way for a quantum computing, with a large number of qubits $n\simeq 100$--1000, far beyond the quantum chaos border. One of the manifestations of such a thermalized non-equilibrated matter is revealed by a strong asymmetry around 90$^\circ $ c.m. of evaporating proton yield in the Bi($\gamma$,p) photonuclear reaction. The effect is described in terms of anomalously slow cross symmetry phase relaxation in highly excited quantum many-body systems with exponentially large Hilbert space dimensions. In the above reaction this phase relaxation is about eight orders of magnitude slower than energy relaxation (thermalization).

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Thermalization in highly excited quantum many-body system does not necessarily mean a complete memory loss of the way the system was formed.	background 0.58	0.17	0.51	asserted 0.85
s1	This effect may pave a way for a quantum computing, with a large number of qubits $n\simeq 100$--1000, far beyond the quantum chaos border.	interpretation 0.96	0.21	0.39	hedged possibility 1.00
s2	One of the manifestations of such a thermalized non-equilibrated matter is revealed by a strong asymmetry around 90$^\circ $ c.m. of evaporating proton yield in the Bi($\gamma$,p) photonuclear reaction.	result 0.96	0.66	0.12	asserted 0.89
s3	The effect is described in terms of anomalously slow cross symmetry phase relaxation in highly excited quantum many-body systems with exponentially large Hilbert space dimensions.	interpretation 0.94	0.54	0.31	asserted 0.99
s4	In the above reaction this phase relaxation is about eight orders of magnitude slower than energy relaxation (thermalization).	result 1.00	0.73	0.20	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.63 · evidence from observation or experiment 0.67.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Scaled experimental angle-integrated spectrum (in arbitrary units) of protons of the Bi(γ,p) photonuclear reaction produced by 24 MeV bremsstrahlung [13]. The line is exponential fit of the scaled spectrum for ε ≤ 8 MeV with the slope (nuclear “temperature”) of 0.55 MeV (see text). 0° 30° 60° 90° 120° 150° 180° 5 10 0 15 20 25 30 # ¾(#) [a.u.]

Figures reproduced from arXiv:quant-ph/0602224 by the authors.

References

Works cited (34)

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of evaporating protons referred to [11, 12] as the continuum co rrelation. Note that such a strong Anomalously Slow Cross Symmetry Phase Relaxation 5 correlation between reduced width amplitudes correspondi ng to the same total spin and parity values but different orbital momenta was experimentally re vealed for a number of compound nuclei in the regime o...

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How the literature uses it

1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [13]

Kun S.Yu., Statistical reactions with memory and therm alized-nonequilibrated nuclear states, Z. Phys. A , 1997, V.357, N 2, 255–269

View on Pith 1997

[2] [1]

Wigner E.P., Characteristic vectors of bordered matric es with infinite dimensions, Ann. Math. , 1955, V.62, N 3, 548–564. Wigner E.P., Characteristic vectors of bordered matrices w ith infinite dimensions II, Ann. Math. , 1957, V.65, N 2, 203–207

View on Pith 1955

[3] [2]

of evaporating protons referred to [11, 12] as the continuum co rrelation. Note that such a strong Anomalously Slow Cross Symmetry Phase Relaxation 5 correlation between reduced width amplitudes correspondi ng to the same total spin and parity values but different orbital momenta was experimentally re vealed for a number of compound nuclei in the regime o...

View on Pith 2005

[4] [3]

Wigner E., Statistical properties of nuclei, Editor J.B . Garg, New York – London, Plenum Press, 1972, p. 11

View on Pith 1972

[5] [4]

Anderson P.W., Basic notions of condensed matter physic s, Frontiers in Physics , Vol. 55, The Benjamin- Cummings, 1984, 71–72

View on Pith 1984

[6] [5]

Guhr T., M¨ uller-Groeling A., Weidenm¨ uller H.A., Rand om matrix theories in quantum physics: common concepts, Phys. Rep. , 1998, V.299, N 4–6, 189–425 (and references therein); cond -mat/9707301

View on Pith arXiv 1998

[7] [6]

Benet L., Izrailev F.M., Seligman T.H., Su´ arez-Moreno A., Semiclassical properties of eigenfunctions and occupation number distribution for a model of two interacti ng particles, Phys. Lett. A , 2000, V.277, N 2, 87–93; chao-dyn/9912035. Anomalously Slow Cross Symmetry Phase Relaxation 7

View on Pith Pith review arXiv 2000

[8] [7]

Benet L., Flores J., Hernandez-Saldana H., Izrailev F.M ., Leyvraz F., Seligman T.H., Fluctuations of wave- functions about their classical average J. Phys. A: Math. Gen. , 2003, V.36, N 5, 1289–1297; nlin.CD/0207039

View on Pith arXiv 2003

[9] [8]

Flores J., Kun S.Yu., Seligman T.H., Slow phase relaxati on as a route to quantum computing beyond the quantum chaos border, Phys. Rev. E , 2005, V.72, N 1, 017201, 4 pages

View on Pith 2005

[10] [9]

Georgeot B., Shepelyansky D.L., Quantum chaos border fo r quantum computing, Phys. Rev. E , 2000, V.62, N 3, 3504–3507; quant-ph/9909074

View on Pith Pith review arXiv 2000

[11] [10]

Shepelyansky D.L., Quantum chaos and quantum computers , in Proceedings of Nobel Symposium on Quan- tum Chaos 2000, Phys. Scripta , 2001, V.90, 112–120; quant-ph/0006073

View on Pith Pith review arXiv 2000

[12] [11]

Bienert M., Flores J., Kun S.Yu., Experimental proposa l for accurate determination of the phase relaxation time in highly excited quantum many-body systems, nucl-ex/ 0508020

View on Pith

[13] [12]

Kun S.Yu., Novel approach to angular distributions in p recompound reactions: Does the Bohr hypothesis always work?, Z. Phys. A , 1994, V.348, N 2, 273–279

View on Pith 1994

[14] [14]

Toms M.E., Stephens W.E., Photoprotons from In, Ce, and Bi, Phys. Rev. , 1953, V.92, N 2, 362–366

View on Pith 1953

[15] [15]

Blatt J.M., Weisskopf V.F., Theoretical nuclear physi cs, New York, Dover Publications, Inc., 1991

View on Pith 1991

[16] [16]

Harvey R.R., Caldwell J.T., Bramblett R.L., Fultz S.C. , Photoneutron cross sections of Pb 206, Pb 207, Pb 208, and Bi 209, Phys. Rev. , 1964, V.136, N 1, B126–B131

View on Pith 1964

[17] [17]

Blann M., Preequilibrium decay, Annu. Rev. Nucl. Sci. , 1975, V.25, 123–166

View on Pith 1975

[18] [18]

Simon A., Theory of polarized particles and gamma rays i n nuclear reactions, Phys. Rev. , 1953, V.92, N 4, 1050–1060

View on Pith 1953

[19] [19]

Racah G., Theory of complex spectra. I, Phys. Rev. , 1942, V.61, N 3–4, 186–197. Racah G., Theory of complex spectra. II, Phys. Rev. , 1942, V.62, N 9–10, 438–462

View on Pith 1942

[20] [20]

Blatt J.M., Biedenharn L.C., The angular distribution s of scattering and reaction cross sections, Rev. Mod. Phys., 1952, V.24, N 4, 258–272

View on Pith 1952

[21] [21]

Kun S.Yu., Ericson fluctuations for the finite spin rel axation times, Phys. Lett. B , 1993, V.319, N 1, 16–22

View on Pith 1993

[22] [22]

Mitchell G.E., Bilpuch E.G., Shriner J.F., Lane A.M., A mplitude correlations in nuclear resonance spec- troscopy, Phys. Rep. , 1985, V.117, N 1, 1–74

View on Pith 1985

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