In an article in Techumin 4 (p. 125), Rav Henkin addresses the practice that in Israel on Yom HaZikaron (and on Yom HaShoah) a siren is sounded throughout the country and everyone stops and observes a moment of silence. He questions this practice on two grounds - (1) Is it considered to be chukat ha-goyim, practices of other nations which we are not supposed to adopt and (2) is it a problem of bittul Torah, taking away from time learning for those who are learning at the time the siren is sounded.
In terms of the first issue, Rav Henkin notes that according to almost all poskim, there is no chukat ha-goyim problem when the practice is one of honor, which this certainly is. The one objector to this allowance is the Gra, who rules that this prohibition applies to any practice that we learn from other nations. However, even if one wanted to rule strictly as per the Gra, Rav Henkin finds two reasons why in this case there would still not be a problem. First, even the Gra only prohibits practices that were created by other nations specifically for them. However, the idea of a moment of silence to honor the deceased is observed in other nations by everyone, even the Jews living in those nations, and thus it does not have the status of a specifically non-Jewish practice. Second, the idea of standing in honor of someone comes up several times in Tanach (such as מפני שיבה תקום) and thus it is actually a Jewish idea. Even if someone wanted to say that the idea of honoring someone by standing when it appears in Tanach does not refer to honoring the deceased, Rav Henkin counters that we do not need that degree of specificity in order to consider this practice to be a Jewish one.
In terms of whether or not this is a ביטול תורה issue, Rav Henkin cites the Gemara in Berachot 53a which discusses whether or not one may interrupt his learning to say "bless you" to someone who has sneezed. While someone learning alone can, the issue is more complicated when we are referring to the learning taking place in a Beit Midrash. There are two main views among the Rishonim, as Rabbeinu Yonah is concerned for this issue when people interrupt learning by speaking, and Rashi feels that there even may be a problem if people interrupt without speaking. Rav Henkin therefore suggests that when the siren wails, a person who is learning in a Beit Midrash should stand silently and think about Torah in memory of those who have fallen, as even when one is learning he sometimes pauses to think about what he is learning.