ZgChlcɂʎqqn̔ÓT_Ci~NX

\\t̐f̏WcN̗\ƃ{[YEtF~vւ̕@̊g

ޗǏqwww

Keywords: aHϕAZgChq͊wAt̐fAWcNA{[YvAtF~v

ʎq̌n_Ci~NX̎pIȌvZ@J邱ƁA܂pđqnƂĂ̗̕ʎqv͊wIȕEۂ𖾂邱Ƃ́Ả݂wEȊw̏dvȉۑłB́AaHϕZgChq͊wiZgChlc܂͂blcj@ɂ锼ÓT_Ci~NXɂāAiPj݌nւ̓KpiQj@̊gÂQ̑ʂ猤sĂB{eł́A

TD M҂PXXWNɉt̃pf̂blc\WcN̗l[1]ǍAPXXX|QOOPN̉Bɂ钆qU[2-3]ɂĊϑEmFꂽƂɂďqׂBɁA

UD T̂blc̓{c}vɏ]]̂blcł邪AꂪɂPXXXNɍlĂ{[YvEtF~v̂߂̂blc[4]ɑ΂āAŋߗʎq͊wIZqpbÂi莮js[5]̂ŁÅTɂďqׂB

blc̖͂̂̒ʂA̔ÓTߎɊÂAx̒`ꂤ鑽Rx̌niN`POQ-PORjɑ΂ĎۗeՂɂ̎ԃ_Ci~NXvZł__łB܂̗_IbɊւĂ͊ɁAblcߎŌvZZgCḧʒu܂͉^ʂ̎ԑ֊֐Aʒu܂͉^ʉZq̃JmjJ֊֐ivەϊ֊֐j

̋ߎɂȂĂ邱ƂĂɎĂ[6]B̌ʁA`_ɂĊϑʂƂĂ̎ԑ֊֐vZłB܂AΗx̋Ɍł̍ŏGlM[g̃_Ci~NXƂ̑ΉĂ[7]B]āAZgChߎ̐藧(Ȃ킿AX̗q̋ԌoHԓIɋǍ݉Ă)󋵉ł́A̗Lɂ͋^̗]n͂ȂB܂M͊wʂ╪z֐̂悤ȐÓIȕɊւĂAblcł͂̃ASY̒œɌvZiblćAԌaH̃TvOƂČaHϕMonte Carlo@܂͌aHϕlc@ĂjB

TD t̃pf̏WcN̗\Ƃ̌̎ɂϑ[1,8] iߐCF.J. Bermejo, C. Cabrillo, S.M. Bennington, B. Fak, M.T. Fernandez-Diaz, P. Verkerk, J. Dawidowski, and R. Fernandez-Pereaj

yTvz t̃pf͑\Iȗʎqt̂ŁAfqde BroglieMIg͕qԋ̒xɋyсAÓT_ɂ舵łȂBIɂÃ_Ci~NXƂ킯AWc^ɂĖȒmĂƂ͌Bt̐fɑ΂M҂̂blc

iPXXWNjȑOɂ́A1973NCarneiro炪sqeU[9]ɂ铮I\q̂sȃXyNgA̕̕q̏Wc^ɊւB̒młBM҂͂blcV~[Vɂĉt̃pf̓I\qvZ[1]ǍʂƂCarneiroƂ̎ʂƂ̔ŕA҂̃f[^̕sS䂦܂苻̂ł͂ȂȂBǍAB̒qO[vŁAeǓʂ̂blčvZʂƈv邱Ƃ񍐂B́ABermejo̊eUiPXXXNj[2]ŁAނ͍L͈͂ɂ킽ĂblčʂƏȂƂʓIɈv錋ʂ񍐂B͍ŋ߂Zoppiɂ񊱏Uł[3]B҂ƂɁAÓTɌɂlcł͎ʂSČȂƂĂB{ł[8]AblčvZʂBermejo̒qʂrBāAÓTɌł̂lcV~[VvZꂽI\qƂ̔rsAWcNɑ΂ʎqʂ𖾂炩ɂB

yrƍl@z fqԑݍpƂĉ肵Silvera-Goldman|eVɑ΂Grueneiseñp[^[i񒲘ap[^[j2.76łAnZʂɑ΂lKX`ɑ΂lɋ߂B]āAt̃pfł͂̃p[^[ṒAKXt̓lAWcN͂܂薾Ăɂ͌ȂƗ\zB

AʂƂblčvZʂ́Aq̗\zƂ͈قȂAĂȏWcN[hicl[hjI\qɌꂽBAÓTlčʂł͌ȃs[NĂȂB́Aqԑݍp̔񒲘â߂ɖxh炬̉ߌN߂łƍliȂ킿AGrueneiseñp[^[ɂ\ĂjB񒲘anł͂blcvZ鎞ԑ֊֐ɂ͒ቷقǁiȂ킿ÓTɌ炸قǁjAmȐUƂƂŋBerne炪qׂĂ邪[10]A{̔r͂ɑ΂鏉߂Ă̏؋^ĂB}́AI\q̃XyNgߌŨXyNg^ɃtBbgۂ̃p[^[ɑ΂ăvbĝłBE}̂ǂ̃vbgłqCMĎʂ́Aɒ̈ŋقǈv悢BAÓTlcł͎ʂƑSقȂĂAWcNɑ΂ʎqʂ킩B

UD BoseFermivɊgblc̍Ē莮[5]iߐCG()Cc_iYjj

yTvz TĎŎg悤ȏ]^̂blcł͑̌n̓{c}vɏ]B́AZgChʂ̂ł鎩RxƂāAÓTIȁiqԍ̃CfbNX̕tj^ɏ]ĎԔW邱ƂƂƂĂB{ł́Ablc@{[YEtF~vɊgāAh{[YEtF~n̔ÓT_Ci~NXhvZi`j@JAǍvZꂽ_Ci~NXIɗLӂȂ̂ł邱ƂƂ_B̕@̔W̉ŁAwES{[YÏk̂̃_Ci~NX̗AGross-PitaevskiiƂ͈q_IȊpxŉ\ɂȂƊ҂ĂB{[YEtF~n̊{IȘgg݂͂ꂪNɎ[4]A{ł́ÂⒼIłoAˉeZqJang-Voth̏xZqiPXXXNj[6]gāAʎq͊wIɋߎ̃xmł̂ɍč\B̊T͈ȉɏqׂ邪ǍʂɂƁÃ{[YEtF~n̂blcŒڌvZA{[YEtF~ńuZgChvi͏]^̃{c}vɂZgChƂ͈ӖقȂj̈ʒu̎ԑ֊֐́A{\EtF~I琬ʎqv͊wn̈ʒuZq̃JmjJ֊֐̈̋ߎɂȂĂ邱ƂꂽB]āA{[YEtF~nblcʎq͊wIϑ(ԑ֊֐)vZł邱Ƃ͓IɎꂽB

yACfAz m̃{]܂̓tF~IΏۂɂ邪Â܂܂ł́Aq̋ʂs\ł邱Ƃ瓦Ȃ߁AÓT_Ci~NXɋA邱ƂłȂBŁA炩̌`Ń{[YEtF~n(n){c}vɏ]niq̋ʂ̂łnjɑΉȂ΂ȂȂBŌnˉeZq

pēm̂̃{c}nɃ}bvBŁA

͔Ԃ̑֐Ui܂͂m̎Rqn̖xsjƋߎBɂāACӂ̉Zq́ijΏ̉ꂽɂĂ̑Ίpai{[YEtF~njAΏ̉ł̑ΊpaɋABΏ͉̉zIȁu[{c}nvɑ΂̂ƍlA̋[{c}nɑ΂blcl邱ƂɂB̑֐ȖΐĐVȃ|eV`B[{c}ńAñn~gjA ɉ̂n~gjAƂĎBZgCh͂̋[{c}nɑ΂Ċeq̋ԌaH̕ψʒuƂēlɒ`BÃZgCĥ܂܌X̃{\AtF~I\Ăƍl͓̂K؂ł͂ȂBJang-Voth̏xZq̎@̋[{c}nɑ΂ēKpāA`Iɋ[{c}n̂blc^𓱏oBɂ̃ZgCḧʒu̎ԑ֊֐[{c}n̈ʒuZq̃JmjJ֊֐̋ߎɂȂĂ邱Ƃ͂ɎꂽBɂ܂ÃJmjJ֊֐AñJmjJ֊֐ƋߎIɓƂ킩B̌ʁA̋ߎŁA[{c}n̂blcɂČni{[YEtF~nj̈ʒuZq̗ʎqv͊wIԑ֊֐iϑʁjvZXL[łB

ȂM[11]ɂ΁Aŋ߁Aʂ̃O[vƓľ_ɎB

[1] K. Kinugawa, Chem. Phys. Lett. 292, 454 (1998).
[2] F.J. Bermejo et al., Phys. Rev. B 60 15154 (1999).
[3] M. Zoppi, D. Colognesi, and M. Celli, Europhys. Lett. 53, 34 (2001).
[4] K. Kinugawa, H. Nagao, and K. Ohta, Chem. Phys. Lett. 307, 187 (1999).
[5] ibid., J. Chem. Phys. 114, 1454 (2001).
[6] S. Jang and G.A. Voth, ibid. 111, 2357 (1999).
[7] (a) R. Ramirez, T. Lopez-Ciudad, and J.C. Noya, Phys. Rev. Lett. 81, 3303 (1998); (b) R. Ramirez and T. Lopez-Ciudad, J. Chem. Phys. 111, 3339 (1999).
[8] F.J. Bermejo, K. Kinugawa et al., Phys. Rev. Lett. 84, 5359 (2000).
[9] K. Carneiro et al. ibid. 30, 481 (1973).
[10] G. Krilov et al., J. Chem. Phys. 111, 9140 (1999).
[11] N.V. Blinov, P.-N. Roy, and G.A. Voth, private communication.

Semiclassical dynamics of quantum many-body molecular systems by path integral centroid molecular dynamics method \\ Prediction of collective excitation in liquid hydrogen and methodological extension of CMD to the Bose and Fermi statistics

Kenichi Kinugawa

Department of Chemistry, Faculty of Science, Nara Womenfs University, Kitauoya-nishi,

Nara 630-8506 (e-mail: kinugawa@cc.nara-wu.ac.jp)

Keywords: path integral, centroid molecular dynamics, liquid hydrogen, Bose statistics, Fermi

statistics

It is an important subject to develop a computational method for real-time dynamics of quantum statistical systems and to apply it to the investigation of dynamical properties of real quantum materials. The semiclassical dynamics obtained from the numerical simulations based on the path integral centroid molecular dynamics (CMD) method is evidently good information of such quantum many-body molecular systems. The present report includes a couple of abstracts of our recent works concerned with (I) the CMD prediction of collective excitation in liquid para-hydrogen [1] prior to the experimental observation in 1999-2001 [2-3]; (II) the reformulation of the CMD extended to Bose-Einstein and Fermi-Dirac statistics by use of quantum-mechanical operator formalism [4,5].

(I) CMD-based prediction of collective excitation in liquid para-hydrogen and the recent observation by neutron experiments [6] (K.K., F.J. Bermejo et al.):

The origin of the well-defined collective excitations found in liquid para-hydrogen by recent experiments is investigated in comparison with the results of the path integral centroid molecular dynamics simulations. The renormalized dispersion frequencies, the damping constants, and the phase velocities observed in the neutron inelastic scattering experiments are in good agreement with those of the centroid molecular dynamics simulations. The persistence of their relatively long lifetimes down to microscopic scales is well accounted for by the centroid molecular dynamics simulations. In contrast, only overdamped excitations are found in calculations carried within the classical limit. This is a first confirmation of recent findings on the predictive capability of the centroid molecular dynamics of highly anharmonic systems. The results provide fully quantitative evidence of quantum effects on the dynamics of a simple liquid.

(II) Reformulation of CMD extended to Bose and Fermi statistics [5] (K.K., H. Nagao, and K. Ohta):

The presently proposed scheme, refined from our previous derivation of Bose/Fermi CMD [4], is aimed at the calculations of not the exact quantum-mechanical dynamics but the semiclassical dynamics under certain approximations. The formalism is based on the projection operator with which the Bose/Fermi system under consideration is mapped onto a particular type of pseudo-Boltzmann system. In such a pseudo-Boltzmann system (a virtual system) the correlation due to the Bose/Fermi statistics is introduced via an extra pseudopotential called permutation potential and its relevant operator. Using the present semiclassical formalism, the time correlation function of centroid position, which is evaluated from the CMD trajectories in the pseudo-Boltzmann system, is an approximation to the Kubo canonical correlation function of position operator of the exact quantum-statistical system composed of bosons or fermions. There is no such apparent relation between the momentum operator and the corresponding centroid.

References [1] K. Kinugawa, Chem. Phys. Lett. 292, 454 (1998). [2] F.J. Bermejo et al., Phys. Rev. B 60 15154 (1999). [3] M. Zoppi, D. Colognesi, and M. Celli, Europhys. Lett. 53, 34 (2001). [4] K. Kinugawa, H. Nagao, and K. Ohta, Chem. Phys. Lett. 307, 187 (1999). [5] ibid., J. Chem. Phys.114, 1454 (2001). [6] F.J. Bermejo, K. Kinugawa et al., Phys. Rev. Lett. 84, 5359 (2000).