λ點

λ點是氦從一般流體氦(I)相變到超流體氦(II)的溫度，在1標準大氣壓下約為2.17 K。氦（I）和氦（II）可以共存的最低壓力是在He氣體−He(I)−He(II)的三相點，是在2.1768 K（−270.9732 °C）及5.048 kPa（0.04982 atm），是該溫度下的飽和蒸氣壓（若在氣封（英語：Hermetic seal）的容器內，純氦氣會在液體表面形成熱平衡）^[1]。氦(I)和氦(II)可以共存的最高壓力是立方晶系氦固體−He(I)−He(II)的三相點，位在1.762 K（−271.388 °C）, 29.725 atm（3,011.9 kPa）^[2]。

λ點的名稱是因為在上述溫度範圍內描繪比熱容和溫度的圖時（在上述的壓力下，例如一大氣壓力），會出現希臘文的字母λ。當溫度接近λ點時，其比熱容會到達其峰值，只有在零重力時才能準確量測到可以說明比熱容發散的臨界指數（為了要讓流體在一體積內的密度是均勻的）。曾在1992年太空船的酬載中量過比λ點低2 nK時的熱容^[3]。

未解決的物理問題：說明He-4在超流體形變時熱容臨界指數

α

理論值和實際值之間的差異原因^[4]

熱容的圖上有出現峰值，而附近的斜率很大，但在該點的值不會趨近無限大，在形變點前後的值都是有限值^[3]。熱容在峰值附近的行為可以用 $C\approx A_{\pm }t^{-\alpha }+B_{\pm }$ 公式表示，其中 $t=|1-T/T_{c}|$ 是對比溫度（reduced temperature）， $T_{c}$ 是Λ點溫度， $A_{\pm },B_{\pm }$ 是常數（在形變點前和形變點後各有一組值）， $α$ 為臨界指數： $\alpha =-0.0127(3)$ ^[3]^[5]。因為在超流體相變時，該指數為負，因此比熱仍為有限值

臨界指數 $α$ 的實際值和最精準的理論判定技術所得值之間，仍有很大的差異^[6]^[4]，這些技術^[7]^[8]^[9]包括高溫膨脹技術、蒙地卡羅方法以及Conformal bootstrapping（英語：Conformal bootstrapping）。

參考資料

^ Donnelly, Russell J.; Barenghi, Carlo F. The Observed Properties of Liquid Helium at the Saturated Vapor Pressure. Journal of Physical and Chemical Reference Data. 1998, 27 (6): 1217–1274. Bibcode:1998JPCRD..27.1217D. doi:10.1063/1.556028.
^ Hoffer, J. K.; Gardner, W. R.; Waterfield, C. G.; Phillips, N. E. Thermodynamic properties of ⁴He. II. The bcc phase and the P-T and VT phase diagrams below 2 K. Journal of Low Temperature Physics. April 1976, 23 (1): 63–102. Bibcode:1976JLTP...23...63H. doi:10.1007/BF00117245.
^ ^3.0 ^3.1 ^3.2 Lipa, J.A.; Swanson, D. R.; Nissen, J. A.; Chui, T. C. P.; Israelsson, U. E. Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point. Physical Review Letters. 1996, 76 (6): 944–7. Bibcode:1996PhRvL..76..944L. doi:10.1103/PhysRevLett.76.944.
^ ^4.0 ^4.1 Rychkov, Slava. Conformal bootstrap and the λ-point specific heat experimental anomaly. Journal Club for Condensed Matter Physics. 2020-01-31 [2024-01-22]. doi:10.36471/JCCM_January_2020_02  . （原始內容存檔於2020-06-09）（英語）.
^ Lipa, J. A.; Nissen, J. A.; Stricker, D. A.; Swanson, D. R.; Chui, T. C. P. Specific heat of liquid helium in zero gravity very near the lambda point. Physical Review B. 2003-11-14, 68 (17): 174518. Bibcode:2003PhRvB..68q4518L. S2CID 55646571. arXiv:cond-mat/0310163  . doi:10.1103/PhysRevB.68.174518.
^ Vicari, Ettore. Critical phenomena and renormalization-group flow of multi-parameter Phi4 theories. Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007) (Regensburg, Germany: Sissa Medialab). 2008-03-21, 42: 023. doi:10.22323/1.042.0023  （英語）.
^ Campostrini, Massimo; Hasenbusch, Martin; Pelissetto, Andrea; Vicari, Ettore. Theoretical estimates of the critical exponents of the superfluid transition in $^{4}\mathrm{He}$ by lattice methods. Physical Review B. 2006-10-06, 74 (14): 144506. S2CID 118924734. arXiv:cond-mat/0605083  . doi:10.1103/PhysRevB.74.144506.
^ Hasenbusch, Martin. Monte Carlo study of an improved clock model in three dimensions. Physical Review B. 2019-12-26, 100 (22): 224517. Bibcode:2019PhRvB.100v4517H. ISSN 2469-9950. S2CID 204509042. arXiv:1910.05916  . doi:10.1103/PhysRevB.100.224517.
^ Chester, Shai M.; Landry, Walter; Liu, Junyu; Poland, David; Simmons-Duffin, David; Su, Ning; Vichi, Alessandro. Carving out OPE space and precise O(2) model critical exponents. Journal of High Energy Physics. 2020, 2020 (6): 142. Bibcode:2020JHEP...06..142C. S2CID 208910721. arXiv:1912.03324  . doi:10.1007/JHEP06(2020)142.

外部連結

What is superfluidity?

[Donnelly-1] Donnelly, Russell J.; Barenghi, Carlo F. The Observed Properties of Liquid Helium at the Saturated Vapor Pressure. Journal of Physical and Chemical Reference Data. 1998, 27 (6): 1217–1274. Bibcode:1998JPCRD..27.1217D. doi:10.1063/1.556028.

[Hoffer-2] Hoffer, J. K.; Gardner, W. R.; Waterfield, C. G.; Phillips, N. E. Thermodynamic properties of ⁴He. II. The bcc phase and the P-T and VT phase diagrams below 2 K. Journal of Low Temperature Physics. April 1976, 23 (1): 63–102. Bibcode:1976JLTP...23...63H. doi:10.1007/BF00117245.

[JPL-3] 3.0 ^3.1 ^3.2 Lipa, J.A.; Swanson, D. R.; Nissen, J. A.; Chui, T. C. P.; Israelsson, U. E. Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point. Physical Review Letters. 1996, 76 (6): 944–7. Bibcode:1996PhRvL..76..944L. doi:10.1103/PhysRevLett.76.944.

[Rychkov-4] 4.0 ^4.1 Rychkov, Slava. Conformal bootstrap and the λ-point specific heat experimental anomaly. Journal Club for Condensed Matter Physics. 2020-01-31 [2024-01-22]. doi:10.36471/JCCM_January_2020_02  . （原始內容存檔於2020-06-09）（英語）.

[5] Lipa, J. A.; Nissen, J. A.; Stricker, D. A.; Swanson, D. R.; Chui, T. C. P. Specific heat of liquid helium in zero gravity very near the lambda point. Physical Review B. 2003-11-14, 68 (17): 174518. Bibcode:2003PhRvB..68q4518L. S2CID 55646571. arXiv:cond-mat/0310163  . doi:10.1103/PhysRevB.68.174518.

[6] Vicari, Ettore. Critical phenomena and renormalization-group flow of multi-parameter Phi4 theories. Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007) (Regensburg, Germany: Sissa Medialab). 2008-03-21, 42: 023. doi:10.22323/1.042.0023  （英語）.

[7] Campostrini, Massimo; Hasenbusch, Martin; Pelissetto, Andrea; Vicari, Ettore. Theoretical estimates of the critical exponents of the superfluid transition in $^{4}\mathrm{He}$ by lattice methods. Physical Review B. 2006-10-06, 74 (14): 144506. S2CID 118924734. arXiv:cond-mat/0605083  . doi:10.1103/PhysRevB.74.144506.

[8] Hasenbusch, Martin. Monte Carlo study of an improved clock model in three dimensions. Physical Review B. 2019-12-26, 100 (22): 224517. Bibcode:2019PhRvB.100v4517H. ISSN 2469-9950. S2CID 204509042. arXiv:1910.05916  . doi:10.1103/PhysRevB.100.224517.

[9] Chester, Shai M.; Landry, Walter; Liu, Junyu; Poland, David; Simmons-Duffin, David; Su, Ning; Vichi, Alessandro. Carving out OPE space and precise O(2) model critical exponents. Journal of High Energy Physics. 2020, 2020 (6): 142. Bibcode:2020JHEP...06..142C. S2CID 208910721. arXiv:1912.03324  . doi:10.1007/JHEP06(2020)142.

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λ點

相關條目

參考資料

外部連結